2.3.45 Problems 4401 to 4500

Table 2.663: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4401	385	\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.314
4402	1627	\begin{align*} x^{2} y^{\prime }&=y^{2}+y x -x^{2} \\ \end{align*}	✓	✓	✓	✓	0.314
4403	4592	\begin{align*} y^{\prime \prime }-2 x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.314
4404	6413	\begin{align*} \sqrt {x}\, y^{\prime \prime }&=y^{{3}/{2}} \\ \end{align*}	✗	✗	✗	✗	0.314
4405	6701	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	0.314
4406	9713	\begin{align*} x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4407	10669	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4408	10966	\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.314
4409	13871	\begin{align*} x^{4} y^{\prime \prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.314
4410	15685	\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3+\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.314
4411	16181	\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.314
4412	17827	\begin{align*} x^{\prime }&=-3 x+6 y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.314
4413	18785	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.314
4414	23243	\begin{align*} y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y&=2 x^{2}+3 \\ \end{align*}	✓	✓	✓	✗	0.314
4415	23414	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.314
4416	23635	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.314
4417	25164	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.314
4418	1091	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.315
4419	2414	\begin{align*} \left (t^{2}+2\right ) y^{\prime \prime }-y^{\prime } t -3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.315
4420	2697	\begin{align*} x^{\prime }&=6 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.315
4421	3406	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.315
4422	6032	\begin{align*} -y-\left (-x^{2}+1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.315
4423	6648	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\left (-x^{2}+2\right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.315
4424	8412	\begin{align*} 1+{x^{\prime }}^{2}&=\frac {a}{y} \\ \end{align*}	✓	✓	✓	✓	0.315
4425	8832	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.315
4426	8900	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.315
4427	8907	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.315
4428	9561	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.315
4429	10481	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.315
4430	10860	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.315
4431	11070	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.315
4432	18694	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.315
4433	18781	\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4434	21496	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.315
4435	21581	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.315
4436	21585	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.315
4437	21877	\begin{align*} 3 y^{\prime \prime }-4 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4438	23009	\begin{align*} 3 y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4439	25083	\begin{align*} y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.315
4440	25105	\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.315
4441	25234	\begin{align*} 4 t^{2} y^{\prime \prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.315
4442	443	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.316
4443	1274	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4444	1397	\begin{align*} y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
4445	3419	\begin{align*} y^{\prime }&=\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.316
4446	5412	\begin{align*} y y^{\prime }+{y^{\prime }}^{2}&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.316
4447	6533	\begin{align*} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	0.316
4448	6762	\begin{align*} 3 y^{\prime \prime \prime }+x y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4449	8338	\begin{align*} y^{\prime }&=\sin \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.316
4450	9355	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
4451	9601	\begin{align*} y^{\prime }+6 y&={\mathrm e}^{4 t} \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.316
4452	10069	\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}	✓	✓	✓	✓	0.316
4453	10138	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.316
4454	10156	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	0.316
4455	10493	\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4456	10688	\begin{align*} 4 y^{\prime \prime } x -y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4457	10708	\begin{align*} x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4458	10907	\begin{align*} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4459	11111	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.316
4460	11126	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.316
4461	15694	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.316
4462	18383	\begin{align*} y^{\prime \prime }&=x^{2} y-y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.316
4463	19244	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.316
4464	20579	\begin{align*} y^{\left (5\right )}-n^{2} y^{\prime \prime \prime }&={\mathrm e}^{a x} \\ \end{align*}	✓	✓	✓	✓	0.316
4465	21270	\begin{align*} x^{\prime \prime }+t x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.316
4466	23673	\begin{align*} x^{3} \left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.316
4467	24603	\begin{align*} 4 y^{\prime \prime }-y&=x +{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.316
4468	25998	\begin{align*} y^{\prime \prime }+4 y&=12 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.316
4469	26576	\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✓	0.316
4470	27642	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&={\mathrm e}^{-4 x}+x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.316
4471	3693	\begin{align*} y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.317
4472	8023	\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.317
4473	10711	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.317
4474	14282	\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.317
4475	21642	\begin{align*} x^{\prime \prime }-s x&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✗	0.317
4476	23253	\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.317
4477	23522	\begin{align*} e i u^{\prime \prime \prime \prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.317
4478	24882	\begin{align*} y^{\prime \prime }-x {y^{\prime }}^{2}&=0 \\ y \left (2\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	0.317
4479	25331	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.317
4480	652	\begin{align*} y^{\prime }&=\left (x -2\right )^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.318
4481	2425	\begin{align*} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t +y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.318
4482	6277	\begin{align*} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (-x +2\right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
4483	6850	\begin{align*} x +y y^{\prime }+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
4484	8021	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=\cos \left (x \right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.318
4485	8484	\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.318
4486	9619	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{t} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.318
4487	10470	\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
4488	10959	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.318
4489	16665	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.318
4490	18429	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=-x+y \\ \end{align*}	✓	✓	✓	✓	0.318
4491	18780	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	0.318
4492	18859	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.318
4493	21721	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.318
4494	23345	\begin{align*} y^{\prime \prime }-i y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.318
4495	24712	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.318
4496	40	\begin{align*} y^{\prime }&=x +\frac {y^{2}}{2} \\ y \left (-2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.319
4497	467	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.319
4498	651	\begin{align*} y^{\prime }&=2 x +1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.319
4499	1398	\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.319
4500	1743	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.319