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Mathematica |
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y-\sin \left (n x \right ) = 0
\]
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\[
{} y^{\prime \prime }+y-a \cos \left (b x \right ) = 0
\]
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\[
{} y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right ) = 0
\]
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\[
{} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0
\]
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\[
{} y^{\prime \prime }+a^{2} y-\cot \left (a x \right ) = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0
\]
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\[
{} y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x} = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0
\]
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\[
{} x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0
\]
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\[
{} x y^{\prime \prime }-x y^{\prime }-y-x \left (1+x \right ) {\mathrm e}^{x} = 0
\]
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\[
{} x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y-a \,x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-v^{2}+x^{2}\right ) y-f \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right ) = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-\ln \left (x \right ) x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {d}{d x}\operatorname {LegendreP}\left (n , x\right ) = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0
\]
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\[
{} x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0
\]
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\[
{} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0
\]
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\[
{} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0
\]
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\[
{} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0
\]
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\[
{} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0
\]
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\[
{} y^{\prime \prime } = -\frac {\left (2 a x +b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (a v x -b \right ) y}{\left (a x +b \right ) x^{2}}+A x
\]
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\[
{} y^{\prime \prime } = -\frac {b y}{x^{2} \left (-a +x \right )^{2}}+c
\]
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\[
{} y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )}
\]
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\[
{} y^{\prime \prime }-6 y^{2}-x = 0
\]
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\[
{} y^{\prime \prime }+y^{2} a +b x +c = 0
\]
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\[
{} y^{\prime \prime }-2 y^{3}-x y+a = 0
\]
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\[
{} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0
\]
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\[
{} y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\]
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\[
{} y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\]
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\[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\]
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\[
{} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\]
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\[
{} y^{\prime \prime }-3 y y^{\prime }-3 y^{2} a -4 a^{2} y-b = 0
\]
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\[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\]
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\[
{} x y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b = 0
\]
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\[
{} x^{2} y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b \,x^{2} = 0
\]
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\[
{} x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0
\]
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\[
{} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\]
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\[
{} 2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0
\]
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\[
{} y y^{\prime \prime }-a = 0
\]
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\[
{} y y^{\prime \prime }-a x = 0
\]
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\[
{} y y^{\prime \prime }-a \,x^{2} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0
\]
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\[
{} y y^{\prime \prime }+y^{2}-a x -b = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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\[
{} 2 y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0
\]
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\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0
\]
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\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\]
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\[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\]
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\[
{} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} 3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\]
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\[
{} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0
\]
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\[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}+a y y^{\prime }+f \left (x \right ) = 0
\]
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\[
{} y^{2} y^{\prime \prime }-a = 0
\]
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\[
{} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x = 0
\]
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\[
{} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\]
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\[
{} x y^{2} y^{\prime \prime }-a = 0
\]
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\[
{} y^{3} y^{\prime \prime }-a = 0
\]
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\[
{} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\]
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\[
{} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\]
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\[
{} \sqrt {y}\, y^{\prime \prime }-a = 0
\]
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\[
{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0
\]
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\[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
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\[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
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\[
{} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\]
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\[
{} y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\]
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\[
{} x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c x \left (-c \,x^{2}+a x +b +1\right ) = 0
\]
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\[
{} x^{2} \left (-a +x \right )^{2} y^{\prime \prime }+b y = c \,x^{2} \left (-a +x \right )^{2}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\]
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