2.3.86 Problems 8501 to 8600

Table 2.703: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8501	2620	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.428
8502	2755	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.428
8503	4016	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }-2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
8504	6450	\begin{align*} y y^{\prime \prime }&=b +a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.428
8505	7081	\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.428
8506	7635	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
8507	8011	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.428
8508	8169	\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align*}	✓	✓	✓	✓	0.428
8509	8182	\begin{align*} 5 y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.428
8510	8257	\begin{align*} y^{\prime } x&=2 x \\ \end{align*}	✓	✓	✓	✓	0.428
8511	8473	\begin{align*} x^{\prime }&=-\lambda _{1} x \\ y^{\prime }&=\lambda _{1} x-\lambda _{2} y \\ \end{align*}	✓	✓	✓	✓	0.428
8512	8488	\begin{align*} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
8513	10086	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\ \end{align*}	✓	✓	✓	✗	0.428
8514	11812	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
8515	16916	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.428
8516	17337	\begin{align*} y-t y^{\prime }&=-2 {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.428
8517	17430	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.428
8518	17433	\begin{align*} y^{\prime \prime }+4 y&=3 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.428
8519	17899	\begin{align*} \tan \left (y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
8520	18431	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.428
8521	18961	\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.428
8522	19201	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{3}+3 x \\ \end{align*}	✓	✓	✓	✓	0.428
8523	19468	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
8524	21876	\begin{align*} 9 y^{\prime \prime }-30 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.428
8525	22706	\begin{align*} y^{\prime \prime \prime \prime }-y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.428
8526	23496	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.428
8527	23591	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-y \\ \end{align*}	✓	✓	✓	✓	0.428
8528	24764	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.428
8529	874	\begin{align*} 2 y^{\prime \prime }+4 y^{\prime }+7 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.429
8530	2602	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \cos \left (t \right )^{2} {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.429
8531	6348	\begin{align*} \left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✗	✗	0.429
8532	7690	\begin{align*} y^{\prime \prime } x +y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.429
8533	11389	\begin{align*} y^{\prime } x -\sqrt {a^{2}-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.429
8534	11494	\begin{align*} \sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4&=0 \\ \end{align*}	✓	✓	✓	✗	0.429
8535	14733	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.429
8536	15730	\begin{align*} y_{1}^{\prime }&=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=y_{1}-2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.429
8537	18728	\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.429
8538	19124	\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	0.429
8539	22155	\begin{align*} y^{\prime \prime }-\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✗	0.429
8540	22158	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.429
8541	22734	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.429
8542	22836	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+\left (x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.429
8543	23524	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	0.429
8544	23600	\begin{align*} x^{\prime }&=4 x-2 y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.429
8545	388	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
8546	855	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.430
8547	974	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=9 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.430
8548	3111	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
8549	3755	\begin{align*} y^{\prime \prime }-y&=2 \tanh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
8550	6320	\begin{align*} y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	0.430
8551	8476	\begin{align*} \left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.430
8552	9777	\begin{align*} y^{\prime \prime }&=x {y^{\prime }}^{2} \\ y \left (2\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	0.430
8553	10939	\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.430
8554	14789	\begin{align*} x^{\prime }&=5 x+3 y \\ y^{\prime }&=4 x+y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.430
8555	16082	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{-\frac {t}{2}} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.430
8556	16884	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.430
8557	16935	\begin{align*} x^{\prime }&=4 x+2 y \\ y^{\prime }&=3 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -21 \\ \end{align*}	✓	✓	✓	✓	0.430
8558	19855	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.430
8559	19984	\begin{align*} y^{2}+x y^{\prime } y-x^{2} {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
8560	21109	\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.430
8561	21530	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.430
8562	21684	\begin{align*} x^{2} y^{\prime \prime }-\left (x +4\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.430
8563	21708	\begin{align*} y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.430
8564	22165	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.430
8565	23589	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.430
8566	24856	\begin{align*} 16 x {y^{\prime }}^{2}+8 y^{\prime } y+y^{6}&=0 \\ \end{align*}	✓	✓	✗	✗	0.430
8567	389	\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
8568	486	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
8569	583	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=10 x-7 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	0.431
8570	1915	\begin{align*} \left (6+4 x \right ) y^{\prime \prime }+\left (2 x +1\right ) y&=0 \\ y \left (-1\right ) &= -1 \\ y^{\prime }\left (-1\right ) &= 2 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	0.431
8571	2833	\begin{align*} x_{1}^{\prime }&=4 x_{2} \\ x_{2}^{\prime }&=-9 x_{1} \\ \end{align*}	✓	✓	✓	✓	0.431
8572	3144	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
8573	3882	\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=3 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ \end{align*}	✓	✓	✓	✓	0.431
8574	3924	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.431
8575	3956	\begin{align*} -2 y+y^{\prime }&=\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.431
8576	4497	\begin{align*} y^{\prime \prime }-y&=\frac {1}{\sinh \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.431
8577	5541	\begin{align*} x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.431
8578	7180	\begin{align*} y^{\prime \prime } x +y^{\prime }+p x y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431
8579	7805	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.431
8580	8285	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.431
8581	8741	\begin{align*} y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.431
8582	10139	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.431
8583	14288	\begin{align*} x^{\prime \prime }-4 x^{\prime }+6 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.431
8584	15123	\begin{align*} y^{\prime }&=\ln \left (y x \right ) \\ \end{align*}	✗	✗	✗	✗	0.431
8585	15181	\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.431
8586	18852	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (t w \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.431
8587	19472	\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.431
8588	20061	\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.431
8589	20180	\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.431
8590	21222	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.431
8591	21745	\begin{align*} x^{\prime }&=4 x-y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.431
8592	25366	\begin{align*} y_{1}^{\prime }&=2 y_{1}-y_{2} \\ y_{2}^{\prime }&=3 y_{1}-2 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.431
8593	15074	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&={\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \\ \end{align*}	✓	✓	✓	✓	0.432
8594	16388	\begin{align*} y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	0.432
8595	16797	\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.432
8596	17298	\begin{align*} t y^{\prime }-{y^{\prime }}^{3}&=y \\ \end{align*}	✓	✓	✓	✗	0.432
8597	20931	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=-5 x \\ \end{align*}	✓	✓	✓	✓	0.432
8598	21643	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432
8599	23039	\begin{align*} y^{\prime \prime }+5 y^{\prime }+8 y&=4 \sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.432
8600	25386	\begin{align*} y_{1}^{\prime }&=5 y_{1}-3 y_{2} \\ y_{2}^{\prime }&=2 y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.432