2.3.54 Problems 5301 to 5400

Table 2.651: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5301	16783	\begin{align*} y^{\prime \prime }+4 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.348
5302	18233	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2+{\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.348
5303	20112	\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.348
5304	21637	\begin{align*} y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.348
5305	23395	\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.348
5306	24542	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.348
5307	449	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.349
5308	2194	\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&={\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.349
5309	3148	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.349
5310	5395	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
5311	5495	\begin{align*} x^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	0.349
5312	6238	\begin{align*} -\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
5313	9231	\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	0.349
5314	10097	\begin{align*} y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \\ \end{align*}	✓	✓	✓	✗	0.349
5315	13066	\begin{align*} x^{\prime }+3 x+4 y&=0 \\ y^{\prime }+2 x+5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
5316	15463	\begin{align*} x^{\prime }&=-x+y \\ y^{\prime }&=-x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (1\right ) &= 0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.349
5317	16184	\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ \end{align*}	✓	✓	✓	✓	0.349
5318	16373	\begin{align*} y^{\prime }+2 x&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.349
5319	16817	\begin{align*} y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.349
5320	18202	\begin{align*} y^{\prime \prime }+y&=4 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.349
5321	18222	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.349
5322	18332	\begin{align*} x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	0.349
5323	18796	\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.349
5324	19494	\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.349
5325	20088	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.349
5326	20508	\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.349
5327	21122	\begin{align*} x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\ \end{align*}	✓	✓	✓	✓	0.349
5328	21154	\begin{align*} x^{\prime \prime }+4 x^{\prime }+x&=k \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.349
5329	25631	\begin{align*} y^{\prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.349
5330	636	\begin{align*} x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.350
5331	5499	\begin{align*} x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.350
5332	5793	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.350
5333	8495	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.350
5334	8962	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.350
5335	10100	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.350
5336	16784	\begin{align*} y^{\prime \prime }+4 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
5337	16792	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
5338	18822	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.350
5339	20419	\begin{align*} \left (-y^{\prime } x +y\right ) \left (y^{\prime }-1\right )&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.350
5340	21492	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.350
5341	21646	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.350
5342	21745	\begin{align*} x^{\prime }&=4 x-y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.350
5343	21947	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.350
5344	22676	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.350
5345	25986	\begin{align*} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.350
5346	26118	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=1+x \,{\mathrm e}^{x}+2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.350
5347	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*}	✓	✓	✓	✓	0.351
5348	612	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.351
5349	613	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.351
5350	2230	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \left (x +1\right ) \\ y \left (-1\right ) &= -6 \\ y^{\prime }\left (-1\right ) &= {\frac {43}{6}} \\ y^{\prime \prime }\left (-1\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	0.351
5351	5926	\begin{align*} -\left (-x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
5352	9443	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.351
5353	10101	\begin{align*} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.351
5354	18687	\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}	✓	✓	✓	✓	0.351
5355	20134	\begin{align*} y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
5356	22130	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.351
5357	22492	\begin{align*} y^{\prime \prime \prime \prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.351
5358	24805	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	0.351
5359	25643	\begin{align*} y^{\prime }&=-\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.351
5360	444	\begin{align*} \left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.352
5361	885	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.352
5362	1314	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.352
5363	1422	\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.352
5364	1449	\begin{align*} x_{1}^{\prime }&=-x_{1}-x_{2} \\ x_{2}^{\prime }&=-\frac {5 x_{2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.352
5365	3267	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.352
5366	4514	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.352
5367	5412	\begin{align*} y y^{\prime }+{y^{\prime }}^{2}&=x \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	0.352
5368	5778	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5369	6694	\begin{align*} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.352
5370	9319	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.352
5371	11389	\begin{align*} y^{\prime } x -\sqrt {a^{2}-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5372	14200	\begin{align*} 2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.352
5373	15482	\begin{align*} x^{\prime }&=x-5 y \\ y^{\prime }&=x-y \\ \end{align*}	✓	✓	✓	✓	0.352
5374	16650	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-8 x} \\ \end{align*}	✓	✓	✓	✓	0.352
5375	16689	\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.352
5376	16738	\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.352
5377	18686	\begin{align*} x^{\prime }&=-\frac {3 x}{2}+y \\ y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\ \end{align*}	✓	✓	✓	✓	0.352
5378	25975	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x}+1 \\ \end{align*}	✓	✓	✓	✓	0.352
5379	3829	\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{2}-x_{1} \\ \end{align*}	✓	✓	✓	✓	0.353
5380	7965	\begin{align*} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}	✓	✓	✗	✗	0.353
5381	8036	\begin{align*} x^{2} y^{\prime \prime }-x \left (3+2 x \right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y&=\left (-x^{2}+6\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.353
5382	8907	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.353
5383	8940	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.353
5384	18916	\begin{align*} y_{1}^{\prime }&=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\ y_{2}^{\prime }&=y_{1}-2 y_{2}+\sin \left (2 t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.353
5385	19853	\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.353
5386	20046	\begin{align*} y^{\prime \prime }-y&=2+5 x \\ \end{align*}	✓	✓	✓	✓	0.353
5387	21772	\begin{align*} x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
5388	21916	\begin{align*} y^{\prime \prime }+y&=\sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.353
5389	23110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.353
5390	24623	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.353
5391	25510	\begin{align*} y^{\prime }&=a t y+q \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.353
5392	25816	\begin{align*} y^{\prime }&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.353
5393	1086	\begin{align*} \left (4 x^{2}+16 x +17\right ) y^{\prime \prime }&=8 y \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= 0 \\ \end{align*} Series expansion around \(x=-2\).	✓	✓	✓	✓	0.354
5394	1526	\begin{align*} y^{\prime }&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.354
5395	5512	\begin{align*} x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5396	7586	\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.354
5397	7820	\begin{align*} 2 y+y^{\prime }&=2 \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.354
5398	8572	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.354
5399	9606	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.354
5400	9992	\begin{align*} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.354