|
ID |
problem |
ODE |
|
1 |
\(y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}\) |
|
|
2 |
\(y^{\prime } = x \left (\cos \left (y\right )+y\right )\) |
|
|
3 |
\(y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}\) |
|
|
4 |
\(y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )\) |
|
|
5 |
\(y^{\prime } = y+1\) |
|
|
6 |
\(y^{\prime } = x +1\) |
|
|
7 |
\(y^{\prime } = x\) |
|
|
8 |
\(y^{\prime } = y\) |
|
|
9 |
\(y^{\prime } = 0\) |
|
|
10 |
\(y^{\prime } = 1+\frac {\sec \left (x \right )}{x}\) |
|
|
11 |
\(y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}\) |
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|
12 |
\(y^{\prime } = \frac {2 y}{x}\) |
|
|
13 |
\(y^{\prime } = \frac {2 y}{x}\) |
|
|
14 |
\(y^{\prime } = \frac {\ln \left (y^{2}+1\right )}{\ln \left (x^{2}+1\right )}\) |
|
|
15 |
\(y^{\prime } = \frac {1}{x}\) |
|
|
16 |
\(y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}\) |
|
|
17 |
\(\frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y = 0\) |
|
|
18 |
\(y^{\prime } = \sqrt {\frac {y+1}{y^{2}}}\) |
|
|
19 |
\(y^{\prime } = \sqrt {1-x^{2}-y^{2}}\) |
|
|
20 |
\(y^{\prime }+\frac {y}{3} = \frac {\left (-2 x +1\right ) y^{4}}{3}\) |
|
|
21 |
\(y^{\prime } = \sqrt {y}+x\) |
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|
23 |
\(x^{2} y^{\prime }+y^{2} = x y y^{\prime }\) |
|
|
24 |
\(y = x y^{\prime }+x^{2} {y^{\prime }}^{2}\) |
|
|
25 |
\(\left (x +y\right ) y^{\prime } = 0\) |
|
|
26 |
\(x y^{\prime } = 0\) |
|
|
27 |
\(\frac {y^{\prime }}{x +y} = 0\) |
|
|
28 |
\(\frac {y^{\prime }}{x} = 0\) |
|
|
29 |
\(y^{\prime } = 0\) |
|
|
30 |
\(y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}\) |
|
|
31 |
\(y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}\) |
|
|
32 |
\(2 t +3 x+\left (x+2\right ) x^{\prime } = 0\) |
|
|
33 |
\(y^{\prime } = \frac {1}{1-y}\) |
|
|
34 |
\(p^{\prime } = a p-b p^{2}\) |
|
|
35 |
\(y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0\) |
|
|
36 |
\(x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}\) |
|
|
37 |
\(x y^{\prime }-2 y+b y^{2} = c \,x^{4}\) |
|
|
38 |
\(x y^{\prime }-y+y^{2} = x^{{2}/{3}}\) |
|
|
39 |
\(u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}\) |
|
|
40 |
\(y^{\prime } y-y = x\) |
|
|
41 |
\(y^{\prime \prime }+2 y^{\prime }+y = 0\) |
|
|
41 |
\(5 y^{\prime \prime }+2 y^{\prime }+4 y = 0\) |
|
|
42 |
\(y^{\prime \prime }+y^{\prime }+4 y = 1\) |
|
|
43 |
\(y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )\) |
|
|
44 |
\(y = x {y^{\prime }}^{2}\) |
|
|
45 |
\(y^{\prime } y = 1-x {y^{\prime }}^{3}\) |
|
|
46 |
\(f^{\prime } = \frac {1}{f}\) |
|
|
47 |
\(t y^{\prime \prime }+4 y^{\prime } = t^{2}\) |
|
|
48 |
\(\left (t^{2}+9\right ) y^{\prime \prime }+2 y^{\prime } t = 0\) |
|
|
49 |
\(t^{2} y^{\prime \prime }-3 y^{\prime } t +5 y = 0\) |
|
|
50 |
\(t y^{\prime \prime }+y^{\prime } = 0\) |
|
|
51 |
\(t^{2} y^{\prime \prime }-2 y^{\prime } = 0\) |
|
|
52 |
\(y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0\) |
|
|
53 |
\(t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0\) |
|
|
54 |
\(y^{\prime \prime } = 0\) |
|
|
55 |
\(y^{\prime \prime } = 1\) |
|
|
56 |
\(y^{\prime \prime } = f \left (t \right )\) |
|
|
57 |
\(y^{\prime \prime } = k\) |
|
|
58 |
\(y^{\prime } = -4 \sin \left (x -y\right )-4\) |
|
|
59 |
\(y^{\prime }+\sin \left (x -y\right ) = 0\) |
|
|
60 |
\(y^{\prime \prime } = 4 \sin \left (x \right )-4\) |
|
|
61 |
\(y y^{\prime \prime } = 0\) |
|
|
62 |
\(y y^{\prime \prime } = 1\) |
|
|
63 |
\(y y^{\prime \prime } = x\) |
|
|
64 |
\(y^{2} y^{\prime \prime } = x\) |
|
|
65 |
\(y^{2} y^{\prime \prime } = 0\) |
|
|
66 |
\(3 y y^{\prime \prime } = \sin \left (x \right )\) |
|
|
67 |
\(3 y y^{\prime \prime }+y = 5\) |
|
|
68 |
\(a y y^{\prime \prime }+b y = c\) |
|
|
69 |
\(a y^{2} y^{\prime \prime }+b y^{2} = c\) |
|
|
70 |
\(a y y^{\prime \prime }+b y = 0\) |
|
|
71 |
\([x^{\prime }\left (t \right ) = 9 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]\) |
|
|
72 |
\([x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )]\) |
|
|
73 |
\([x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right )]\) |
|
|
74 |
\([x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )]\) |
|
|
75 |
\([x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]\) |
|
|
76 |
\([x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )]\) |
|
|
77 |
\(x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x\) |
|
|
78 |
\(\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x\) |
|
|
78 |
\(\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x\) |
|
|
79 |
\(y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}\) |
|
|
80 |
\(y^{\prime } = x^{2}+y^{2}\) |
|
|
81 |
\(y^{\prime } = 2 \sqrt {y}\) |
|
|
82 |
\(z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}\) |
|
|
83 |
\(y^{\prime } = \sqrt {1-y^{2}}\) |
|
|
84 |
\(y^{\prime } = x^{2}+y^{2}-1\) |
|
|
85 |
\(y^{\prime } = 2 y \left (x \sqrt {y}-1\right )\) |
|
|
86 |
\(y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}\) |
|
|
87 |
\(y^{\prime \prime }+y^{\prime }+y = 0\) |
|
|
88 |
\(y^{\prime \prime }+y^{\prime }+y = 0\) |
|
|
88 |
\(y^{\prime \prime }+y^{\prime }+y = 0\) |
|
|
89 |
\(y^{\prime \prime }-y^{\prime } y = 2 x\) |
|
|
90 |
\(y^{\prime }-y^{2}-x -x^{2} = 0\) |
|
|
ID |
problem |
ODE |
|
1 |
\(y^{\prime \prime }-x y^{\prime }-x y-x = 0\) |
|
|
2 |
\(y^{\prime \prime }-x y^{\prime }-x y-2 x = 0\) |
|
|
3 |
\(y^{\prime \prime }-x y^{\prime }-x y-3 x = 0\) |
|
|
4 |
\(y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0\) |
|
|
5 |
\(y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0\) |
|
|
6 |
\(y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0\) |
|
|
7 |
\(y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0\) |
|
|
8 |
\(y^{\prime \prime }-x y^{\prime }-x y-x = 0\) |
|
|
9 |
\(y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0\) |
|
|
10 |
\(y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0\) |
|
|
11 |
\(y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0\) |
|
|
12 |
\(y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0\) |
|
|
13 |
\(y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0\) |
|
|
14 |
\(y^{\prime \prime }-y^{\prime }-x y-x = 0\) |
|
|
15 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0\) |
|
|
16 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0\) |
|
|
16 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0\) |
|
|
17 |
\(y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0\) |
|
|
18 |
\(y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0\) |
|
|
19 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0\) |
|
|
20 |
\(y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0\) |
|
|
21 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0\) |
|
|
22 |
\(y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0\) |
|
|
23 |
\(y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0\) |
|
|
24 |
\(y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0\) |
|
|
25 |
\(y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0\) |
|
|
26 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0\) |
|
|
27 |
\(y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0\) |
|
|
28 |
\(y^{\prime \prime }-x y-x^{3}+2 = 0\) |
|
|
29 |
\(y^{\prime \prime }-x y-x^{6}+64 = 0\) |
|
|
30 |
\(y^{\prime \prime }-x y-x = 0\) |
|
|
31 |
\(y^{\prime \prime }-x y-x^{2} = 0\) |
|
|
32 |
\(y^{\prime \prime }-x y-x^{3} = 0\) |
|
|
33 |
\(y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0\) |
|
|
34 |
\(y^{\prime \prime }-x^{2} y-x^{2} = 0\) |
|
|
35 |
\(y^{\prime \prime }-x^{2} y-x^{3} = 0\) |
|
|
36 |
\(y^{\prime \prime }-x^{2} y-x^{4} = 0\) |
|
|
37 |
\(y^{\prime \prime }-x^{2} y-x^{4}+2 = 0\) |
|
|
38 |
\(y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0\) |
|
|
39 |
\(y^{\prime \prime }-x^{3} y-x^{3} = 0\) |
|
|
40 |
\(y^{\prime \prime }-x^{3} y-x^{4} = 0\) |
|
|
41 |
\(y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0\) |
|
|
42 |
\(y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0\) |
|
|
43 |
\(y^{\prime \prime }-x y^{\prime }-x y-x = 0\) |
|
|
44 |
\(y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0\) |
|
|
45 |
\(y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0\) |
|
|
46 |
\(y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0\) |
|
|
47 |
\(y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0\) |
|
|
48 |
\(y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0\) |
|
|
49 |
\(y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0\) |
|
|
50 |
\(y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0\) |
|
|
51 |
\(y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0\) |
|
|
52 |
\(y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0\) |
|
|
50 |
\(y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0\) |
|
|
ID |
problem |
ODE |
|
1 |
\(y^{\prime \prime }+c y^{\prime }+k y = 0\) |
|
|
2 |
\(w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}\) |
|
|
3 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
4 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
5 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
6 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
7 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
8 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
9 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
10 |
\(y^{\prime \prime }+y = \sin \left (x \right )\) |
|
|
11 |
\(y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )\) |
|
|
12 |
\(y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )\) |
|
|
13 |
\(y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )\) |
|
|
14 |
\(y^{\prime \prime \prime }+y^{\prime }+y = x\) |
|
|
15 |
\(x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1\) |
|
|
16 |
\(x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x\) |
|
|
17 |
\(x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x\) |
|
|
18 |
\(x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0\) |
|
|
19 |
\(x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x\) |
|
|
20 |
\(5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y = 0\) |
|
|
21 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0\) |
|
|
22 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x\) |
|
|
23 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1\) |
|
|
24 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0\) |
|
|
25 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0\) |
|
|
26 |
\(y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0\) |
|
|
27 |
\(\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0\) |
|
|
28 |
\(y^{\prime } = {\mathrm e}^{-\frac {y}{x}}\) |
|
|
29 |
\(y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x}\) |
|
|
30 |
\(4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right )\) |
|
|
31 |
\(v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3}\) |
|
|
ID |
problem |
ODE |
|
1 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 0\) |
|
|
2 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1\) |
|
|
3 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x +1\) |
|
|
4 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x\) |
|
|
5 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+x +1\) |
|
|
6 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}\) |
|
|
7 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+1\) |
|
|
8 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{4}\) |
|
|
9 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )\) |
|
|
10 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1+\sin \left (x \right )\) |
|
|
11 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x \sin \left (x \right )\) |
|
|
12 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )+\sin \left (x \right )\) |
|
|
13 |
\(x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0\) |
|
|
14 |
\(\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0\) |
|
|
15 |
\(\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0\) |
|
|
16 |
\(\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0\) |
|
|
17 |
\(x y^{\prime \prime }+2 y^{\prime }+x y = 0\) |
|
|
18 |
\(2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = x^{2}+2 x\) |
|
|
19 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1\) |
|
|
20 |
\(2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1\) |
|
|
21 |
\(y^{\prime \prime }+\left (x -6\right ) y = 0\) |
|
|
22 |
\(x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0\) |
|
|
23 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )\) |
|
|
24 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )\) |
|
|
24 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )\) |
|
|
24 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )\) |
|
|
24 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}\) |
|
|
24 |
\(2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \ln \left (x \right )\) |
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25 |
\(2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0\) |
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26 |
\(x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0\) |
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27 |
\(x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0\) |
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|
28 |
\({y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}\) |
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|
29 |
\(\left (y-2 x y^{\prime }\right )^{2} = {y^{\prime }}^{3}\) |
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31 |
\(x^{2} y^{\prime \prime }+y = 0\) |
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32 |
\(x y^{\prime \prime }+y^{\prime }-y = 0\) |
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33 |
\(4 x y^{\prime \prime }+2 y^{\prime }+y = 0\) |
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|
34 |
\(x y^{\prime \prime }+y^{\prime }-y = 0\) |
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|
35 |
\(x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0\) |
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36 |
\(x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0\) |
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37 |
\(x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0\) |
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|
38 |
\(2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0\) |
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|
39 |
\(2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y = 0\) |
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|
40 |
\(2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right )\) |
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|
41 |
\(2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x \sin \left (x \right )\) |
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|
42 |
\(2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \cos \left (x \right ) \sin \left (x \right )\) |
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|
43 |
\(2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x^{3}+x \sin \left (x \right )\) |
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|
44 |
\(\cos \left (x \right ) y^{\prime \prime }+2 x y^{\prime }-x y = 0\) |
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|
45 |
\(x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0\) |
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|
46 |
\(x^{2} y^{\prime \prime }+x y^{\prime }-x y = 0\) |
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|
47 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
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|
48 |
\(\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0\) |
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|
49 |
\(x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0\) |
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|
50 |
\(x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y = 0\) |
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|
51 |
\(x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0\) |
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52 |
\(x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0\) |
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|
53 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
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|
54 |
\(x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0\) |
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|
55 |
\(2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0\) |
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|
56 |
\(2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0\) |
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|
57 |
\(x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0\) |
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|
58 |
\(x^{2} y^{\prime \prime }-x y = 0\) |
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|
59 |
\(\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}\) |
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|
60 |
\(y^{\prime } = y \left (1-y^{2}\right )\) |
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61 |
\(\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}\) |
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|
62 |
\(\frac {x y^{\prime \prime }}{1-x}+x y = 0\) |
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|
63 |
\(\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )\) |
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|
64 |
\(\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0\) |
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|
65 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
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|
66 |
\(y^{\prime \prime }+\left (x -1\right ) y = 0\) |
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|
67 |
\([x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+2 t +1, y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+3 t -1]\) |
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|
68 |
\(y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right )\) |
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|
69 |
\(y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0\) |
|
|
ID |
problem |
ODE |
|
1 |
\(y^{\prime \prime } = A y^{{2}/{3}}\) |
|
|
2 |
\(y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0\) |
|
|
3 |
\(y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y = 0\) |
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|
4 |
\(x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0\) |
|
|
5 |
\(4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}\) |
|
|
6 |
\(x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}\) |
|
|
7 |
\(y^{\prime }+y = \frac {1}{x}\) |
|
|
8 |
\(y^{\prime }+y = \frac {1}{x^{2}}\) |
|
|
9 |
\(x y^{\prime }+y = 0\) |
|
|
10 |
\(y^{\prime } = \frac {1}{x}\) |
|
|
11 |
\(y^{\prime \prime } = \frac {1}{x}\) |
|
|
12 |
\(y^{\prime \prime }+y^{\prime } = \frac {1}{x}\) |
|
|
13 |
\(y^{\prime \prime }+y = \frac {1}{x}\) |
|
|
14 |
\(y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}\) |
|
|
15 |
\(h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2}\) |
|
|
16 |
\(y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x}\) |
|
|
17 |
\(y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2}\) |
|
|
18 |
\(y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )}\) |
|
|
19 |
\(y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}\) |
|
|
20 |
\(x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0\) |
|
|
21 |
\(x^{2} y^{\prime }+{\mathrm e}^{-y} = 0\) |
|
|
22 |
\(y^{\prime \prime }+{\mathrm e}^{y} = 0\) |
|
|
23 |
\(y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6}\) |
|