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	8130	\begin{align*} y^{\prime \prime }+2 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.353
4402	10468	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.353
4403	16021	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.353
4404	20512	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.353
4405	26025	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.353
4406	26942	\begin{align*} y^{\prime \prime }+16 y^{\prime }+64 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
4407	435	\begin{align*} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.354
4408	6633	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.354
4409	7981	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
4410	26014	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }&=2 x^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.354
4411	26075	\begin{align*} y_{1}^{\prime }&=4 y_{1}-y_{2} \\ y_{2}^{\prime }&=y_{1}+2 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.354
4412	27567	\begin{align*} -y^{\prime }+x y^{\prime \prime }&=x^{2} y y^{\prime } \\ \end{align*}	✗	✓	✓	✗	0.354
4413	27648	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.354
4414	1067	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
4415	1092	\begin{align*} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
4416	10184	\begin{align*} y^{\prime \prime }+\left (-6+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.355
4417	10662	\begin{align*} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.355
4418	18296	\begin{align*} x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
4419	19775	\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
4420	21292	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-y+\delta \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.355
4421	22102	\begin{align*} y^{\prime \prime }-y^{\prime }-30 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
4422	22243	\begin{align*} y^{\prime }+5 y&=0 \\ y \left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.355
4423	22313	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
4424	23283	\begin{align*} 3 y^{\prime \prime }+48 y^{\prime }+192 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
4425	23551	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	0.355
4426	23781	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{1} \\ \end{align*}	✓	✓	✓	✓	0.355
4427	25165	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.355
4428	26937	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.355
4429	437	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
4430	1371	\begin{align*} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
4431	4063	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.356
4432	6643	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.356
4433	7451	\begin{align*} y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
4434	8985	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.356
4435	17823	\begin{align*} x^{\prime }&=0 \\ y^{\prime }&=-2 y \\ \end{align*}	✓	✓	✓	✓	0.356
4436	19123	\begin{align*} y&=x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.356
4437	23592	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.356
4438	26483	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.356
4439	1044	\begin{align*} 2 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.357
4440	10642	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.357
4441	26716	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.357
4442	26731	\begin{align*} x^{\prime }&=2 x-9 y \\ y^{\prime }&=x+8 y \\ \end{align*}	✓	✓	✓	✓	0.357
4443	27110	\(\left [\begin {array}{cc} 0 & -1 \\ 4 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.357
4444	3570	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4445	3791	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.358
4446	7360	\begin{align*} x y^{\prime }&=y x +y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.358
4447	7459	\begin{align*} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4448	15096	\begin{align*} y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.358
4449	16412	\begin{align*} y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.358
4450	20488	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.358
4451	21874	\begin{align*} y^{\prime \prime }-12 y^{\prime }+35 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4452	21946	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.358
4453	23359	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4454	23696	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.358
4455	25070	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.358
4456	25078	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.358
4457	25629	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.358
4458	26720	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.358
4459	862	\begin{align*} \frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.359
4460	1096	\begin{align*} y^{\prime \prime }-2 x y^{\prime }+2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4461	1789	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=x^{2} \\ y \left (1\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (1\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	0.359
4462	4062	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4463	4492	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime }-4 y&=50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.359
4464	5524	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.359
4465	7632	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4466	9227	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.359
4467	16026	\begin{align*} x^{\prime }&=2 x+y \\ y^{\prime }&=-x+4 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.359
4468	16062	\begin{align*} x^{\prime }&=2 x \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.359
4469	17699	\begin{align*} y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✗	0.359
4470	17759	\begin{align*} y^{\prime \prime \prime }-12 y^{\prime }-16 y&={\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.359
4471	20493	\begin{align*} x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.359
4472	23062	\begin{align*} r^{\prime }&=0 \\ r \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.359
4473	23786	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.359
4474	25630	\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.359
4475	27051	\begin{align*} y_{1}^{\prime }-2 y_{2}^{\prime }+3 y_{1}&=0 \\ y_{1}-4 y_{2}^{\prime }+3 y_{3}&=t \\ y_{1}-2 y_{2}^{\prime }+3 y_{3}^{\prime }&=-1 \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 0 \\ y_{2} \left (0\right ) &= 0 \\ y_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.359
4476	27067	\begin{align*} y^{\prime \prime }+x y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359
4477	27092	\(\left [\begin {array}{cc} 1 & -6 \\ 2 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.359
4478	27589	\begin{align*} {y^{\prime }}^{2}+2 x y y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.359
4479	2616	\begin{align*} y^{\prime \prime }-t^{3} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.360
4480	7074	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.360
4481	7378	\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.360
4482	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.	✓	✓	✓	✓	0.360
4483	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*}	✓	✓	✓	✗	0.360
4484	16028	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.360
4485	16500	\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.360
4486	16716	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.360
4487	19686	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.360
4488	23362	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.360
4489	23934	\begin{align*} y^{\prime }&=z \\ z^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.360
4490	24057	\begin{align*} 2 y^{\prime }+y&={\mathrm e}^{x} \\ y \left (2\right ) &= \frac {4 \,{\mathrm e}^{2}}{3} \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.360
4491	27573	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{x^{2}}&=\frac {{y^{\prime }}^{2}}{y} \\ \end{align*}	✗	✓	✓	✗	0.360
4492	277	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4493	1738	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= k_{0} \\ y^{\prime }\left (0\right ) &= k_{1} \\ \end{align*}	✓	✓	✓	✓	0.361
4494	2611	\begin{align*} y^{\prime \prime }-y t&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.361
4495	6627	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.361
4496	6632	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=\left (x -1\right ) x \\ \end{align*}	✓	✓	✓	✓	0.361
4497	9621	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.361
4498	12563	\begin{align*} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.361
4499	12705	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {\left (x -1\right ) y}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	0.361
4500	16703	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.361