2.3.75 Problems 7401 to 7500

Table 2.723: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
7401	9246	\begin{align*} 4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.931
7402	10508	\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.931
7403	10529	\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.931
7404	15331	\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.931
7405	15831	\begin{align*} y^{\prime }&=t^{2}-2 \\ \end{align*}	✓	✓	✓	✓	0.931
7406	16515	\begin{align*} y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.931
7407	17605	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sec \left (t \right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✗	✓	✓	0.931
7408	19242	\begin{align*} y^{\prime } x&=1 \\ \end{align*}	✓	✓	✓	✓	0.931
7409	19262	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=1 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.931
7410	20205	\begin{align*} x^{\prime }+2 x+y^{\prime }+y&=0 \\ 5 x+y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.931
7411	21139	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=2 t +{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.931
7412	21587	\begin{align*} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime }&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.931
7413	923	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.932
7414	5785	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.932
7415	9245	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.932
7416	7090	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.933
7417	1437	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.934
7418	1454	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-2 \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.934
7419	2291	\begin{align*} y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }&=y_{2}+y_{3} \\ y_{3}^{\prime }&=y_{1}+y_{3} \\ \end{align*}	✓	✓	✓	✓	0.934
7420	4486	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.934
7421	21132	\begin{align*} x^{\prime \prime }+x&=t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	0.934
7422	21146	\begin{align*} x^{\prime \prime }-x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.934
7423	23386	\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.934
7424	23609	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=-3 y \\ \end{align*}	✓	✓	✓	✓	0.934
7425	24923	\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ \end{align*}	✓	✓	✓	✓	0.934
7426	25099	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.934
7427	620	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.935
7428	6394	\begin{align*} 2+4 y^{\prime } x +x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.935
7429	7291	\begin{align*} y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.935
7430	7906	\begin{align*} y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.935
7431	19502	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.935
7432	19840	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.935
7433	21212	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.935
7434	21222	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.935
7435	21514	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.935
7436	24922	\begin{align*} y^{\prime }&=t +3 \\ \end{align*}	✓	✓	✓	✓	0.935
7437	25101	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.935
7438	1975	\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.936
7439	3873	\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.936
7440	5771	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \left (3 x^{2}+2 x +1\right ) \\ \end{align*}	✓	✓	✓	✓	0.936
7441	24681	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=4 x^{3}+2 x \\ \end{align*}	✓	✓	✓	✓	0.936
7442	464	\begin{align*} \left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.937
7443	644	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }&=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.937
7444	1998	\begin{align*} 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 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.937
7445	4565	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.937
7446	4571	\begin{align*} x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.937
7447	5414	\begin{align*} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.937
7448	7294	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.937
7449	9172	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.937
7450	9262	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.937
7451	11739	\begin{align*} \left (x^{2}+a \right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}+b&=0 \\ \end{align*}	✓	✓	✓	✗	0.937
7452	14837	\begin{align*} t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.937
7453	16195	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.937
7454	1353	\begin{align*} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✗	0.938
7455	3739	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.938
7456	4067	\begin{align*} 2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.938
7457	4478	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \left (x +1\right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.938
7458	5466	\begin{align*} x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.938
7459	5468	\begin{align*} x {y^{\prime }}^{2}+\left (a +b x -y\right ) y^{\prime }-b y&=0 \\ \end{align*}	✓	✓	✓	✗	0.938
7460	9254	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.938
7461	9603	\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.938
7462	13876	\begin{align*} x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	0.938
7463	14358	\begin{align*} x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.938
7464	15267	\begin{align*} x^{\prime }-x+2 y&=0 \\ y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	0.938
7465	15443	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.938
7466	18253	\begin{align*} y^{\prime \prime }+y^{\prime }+y+1&=\sin \left (x \right )+x +x^{2} \\ \end{align*}	✓	✓	✓	✓	0.938
7467	3752	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.939
7468	12506	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-\left (1+3 x \right ) y^{\prime }-\left (x^{2}-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.939
7469	1972	\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.940
7470	1974	\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.940
7471	2588	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\sqrt {1+t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.940
7472	7805	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.940
7473	7824	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.940
7474	14875	\begin{align*} T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.940
7475	20360	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.940
7476	22320	\begin{align*} y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\ y \left (0\right ) &= -4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.940
7477	22762	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.940
7478	2080	\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.941
7479	8911	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.941
7480	16728	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.941
7481	17709	\begin{align*} 2 y^{\prime \prime } x -5 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.941
7482	18000	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {y^{\prime }}{y}} \\ \end{align*}	✓	✓	✓	✗	0.941
7483	19210	\begin{align*} y^{\prime }&=y+z \\ z^{\prime }&=y+z+x \\ \end{align*}	✓	✓	✓	✓	0.941
7484	26049	\begin{align*} \left (y^{\prime } x +y\right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	0.941
7485	17489	\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.942
7486	9617	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.943
7487	9805	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.943
7488	12320	\begin{align*} y^{\prime \prime }-y^{\prime } x +\left (-1+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.943
7489	16314	\begin{align*} {\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.943
7490	19577	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.943
7491	21517	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	0.943
7492	6164	\begin{align*} \left (x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.944
7493	8143	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.944
7494	10518	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.944
7495	14401	\begin{align*} x^{\prime }&=-5 x+3 y \\ y^{\prime }&=2 x-10 y \\ \end{align*}	✓	✓	✓	✓	0.944
7496	14822	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.944
7497	17997	\begin{align*} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.944
7498	20082	\begin{align*} y^{\prime \prime }-2 y^{\prime }+4 y&={\mathrm e}^{x} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.944
7499	20927	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-3 x \\ \end{align*}	✓	✓	✓	✓	0.944
7500	14639	\begin{align*} 4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.945