2.3.44 Problems 4301 to 4400

Table 2.661: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4301	2783	\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*}	✓	✓	✓	✓	0.309
4302	3415	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.309
4303	4560	\begin{align*} 2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.309
4304	5885	\begin{align*} 3 y-8 y^{\prime }+4 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4305	8491	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.309
4306	8636	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\ y \left (\frac {3}{2}\right ) &= 4 \\ y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.309
4307	9222	\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4308	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.	✓	✓	✓	✓	0.309
4309	9716	\begin{align*} x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4310	10675	\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4311	10866	\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4312	11203	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.309
4313	15324	\begin{align*} x^{\prime }+y^{\prime }+x&=0 \\ x^{\prime }-x+2 y^{\prime }&={\mathrm e}^{-t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.309
4314	16577	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4315	16803	\begin{align*} y^{\prime \prime }&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.309
4316	18381	\begin{align*} y^{\prime \prime }-y^{\prime } x +y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.309
4317	20332	\begin{align*} 9 x^{\prime \prime }+18 x^{\prime }-16 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4318	21709	\begin{align*} y^{\prime }+2 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.309
4319	21727	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.309
4320	21866	\begin{align*} {y^{\prime }}^{2}+y&=y^{\prime } x +1 \\ \end{align*}	✓	✓	✓	✓	0.309
4321	21952	\begin{align*} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\ \end{align*}	✗	✗	✗	✗	0.309
4322	23022	\begin{align*} y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi \sqrt {3}}{3}\right ) &= 5 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{2}} \\ \end{align*}	✓	✓	✓	✓	0.309
4323	23270	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4324	23390	\begin{align*} 2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-12 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4325	24585	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.309
4326	25106	\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.309
4327	25643	\begin{align*} y^{\prime }&=-\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.309
4328	25816	\begin{align*} y^{\prime }&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.309
4329	26626	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }&=6 y \\ \end{align*}	✓	✓	✓	✓	0.309
4330	26819	\begin{align*} x^{\prime \prime }-5 x^{\prime }+6 x&=12 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.309
4331	27639	\begin{align*} y^{\prime \prime }+y&=4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.309
4332	3937	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.310
4333	4090	\begin{align*} y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.310
4334	6187	\begin{align*} x^{3} y^{\prime \prime }&=b x +a \\ \end{align*}	✓	✓	✓	✓	0.310
4335	6459	\begin{align*} 2 {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.310
4336	8131	\begin{align*} y^{\prime \prime }-y x&=\frac {1}{1-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.310
4337	8489	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.310
4338	9170	\begin{align*} y^{\prime } x +y+3 x^{3} y^{4} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4339	9824	\begin{align*} x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.310
4340	10399	\begin{align*} y^{\prime \prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.310
4341	10627	\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.310
4342	10773	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.310
4343	12594	\begin{align*} y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \\ \end{align*}	✓	✓	✓	✗	0.310
4344	15149	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.310
4345	18918	\begin{align*} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.310
4346	20707	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	0.310
4347	21111	\begin{align*} x^{\prime \prime }+2 x^{\prime }-15 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.310
4348	24537	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=27 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.310
4349	1060	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.311
4350	1077	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.311
4351	7262	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.311
4352	9359	\begin{align*} y^{\prime } x&=y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.311
4353	11275	\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}	✓	✓	✓	✗	0.311
4354	13771	\begin{align*} a y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.311
4355	16663	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}	✓	✓	✓	✓	0.311
4356	17745	\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.311
4357	22261	\begin{align*} y^{\prime }-z&=0 \\ y-z^{\prime }&=0 \\ \end{align*} With initial conditions \begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.311
4358	22691	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.311
4359	24460	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.311
4360	26159	\begin{align*} {y^{\prime }}^{2}+{\mathrm e}^{y^{\prime }}&=x \\ \end{align*}	✓	✓	✓	✗	0.311
4361	342	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.312
4362	1757	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {4}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.312
4363	2798	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.312
4364	5782	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4365	6436	\begin{align*} y y^{\prime \prime }&=-2 y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	0.312
4366	8067	\begin{align*} \left (1-x \right ) y^{\prime }&=x^{2}-y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.312
4367	8358	\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	0.312
4368	8895	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.312
4369	9353	\begin{align*} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.312
4370	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.	✓	✓	✓	✓	0.312
4371	10797	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.312
4372	10953	\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.312
4373	10980	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.312
4374	18028	\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4375	18380	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.312
4376	18759	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4377	19436	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4378	19466	\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.312
4379	21112	\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.312
4380	21221	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.312
4381	21745	\begin{align*} x^{\prime }&=4 x-y \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.312
4382	23413	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.312
4383	24538	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-6 x^{2}-8 x +4 \\ \end{align*}	✓	✓	✓	✓	0.312
4384	25967	\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\ \end{align*}	✓	✓	✓	✓	0.312
4385	26364	\begin{align*} x&=\sin \left (y^{\prime }\right )+y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.312
4386	26833	\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=t^{2} {\mathrm e}^{-2 t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.312
4387	27765	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.312
4388	393	\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.313
4389	395	\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	0.313
4390	6644	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=\cosh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.313
4391	9177	\begin{align*} y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
4392	10630	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
4393	10839	\begin{align*} y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.313
4394	15210	\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ y^{\prime \prime }\left (0\right ) &= 8 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.313
4395	20050	\begin{align*} y^{\prime \prime \prime }-y&=\left ({\mathrm e}^{x}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.313
4396	20124	\begin{align*} x^{2} y^{\prime \prime \prime \prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.313
4397	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*}	✓	✓	✓	✓	0.313
4398	21657	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.313
4399	27641	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	0.313
4400	27667	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.313