2.3.44 Problems 4301 to 4400

Table 2.619: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4301	2265	\begin{align*} y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\ y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 6 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.336
4302	4177	\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.336
4303	4528	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4304	5693	\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
4305	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.	✓	✓	✓	✓	0.336
4306	9727	\begin{align*} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.336
4307	11200	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
4308	14732	\begin{align*} y^{\prime \prime }-y^{\prime } x +\left (3 x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
4309	18909	\begin{align*} y^{\prime \prime \prime \prime }-9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4310	19125	\begin{align*} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.336
4311	20934	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.336
4312	22934	\begin{align*} x^{\prime }+5 x-4 y&=0 \\ y^{\prime }-x+2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.336
4313	23443	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.336
4314	23633	\begin{align*} y^{\prime }-3 y&=13 \cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4315	23660	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.336
4316	23788	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.336
4317	1416	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.337
4318	1419	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.337
4319	2414	\begin{align*} \left (t^{2}+2\right ) y^{\prime \prime }-y^{\prime } t -3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.337
4320	12859	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\ \end{align*}	✗	✗	✗	✗	0.337
4321	16013	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.337
4322	23654	\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.337
4323	25747	\begin{align*} {y^{\prime }}^{2}&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.337
4324	978	\begin{align*} x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.338
4325	1383	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4326	2041	\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338
4327	6437	\begin{align*} y-y^{\prime } x +{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	0.338
4328	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.	✓	✓	✓	✓	0.338
4329	18083	\begin{align*} {y^{\prime }}^{4}&=1 \\ \end{align*}	✓	✓	✓	✓	0.338
4330	18675	\begin{align*} x^{\prime }&=a x+y \\ y^{\prime }&=-x+a y \\ \end{align*}	✓	✓	✓	✓	0.338
4331	19050	\begin{align*} x_{1}^{\prime }&=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }&=x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.338
4332	21211	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= a \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.338
4333	23770	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.338
4334	1370	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4335	4170	\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=y_{1} \\ \end{align*}	✓	✓	✓	✓	0.339
4336	8197	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=5 x+3 y \\ \end{align*}	✓	✓	✓	✓	0.339
4337	8845	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.339
4338	14377	\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.339
4339	14735	\begin{align*} \left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4340	14853	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.339
4341	15470	\begin{align*} x^{\prime }&=3 x-y \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.339
4342	18737	\begin{align*} y^{\prime \prime }-\frac {t}{y}&=\frac {1}{\pi } \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= y_{1} \\ \end{align*}	✗	✗	✓	✗	0.339
4343	18959	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.339
4344	20884	\begin{align*} y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.339
4345	420	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4346	3938	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.340
4347	5637	\begin{align*} {y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 y^{\prime } y^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4348	10331	\begin{align*} x^{\prime }+y^{\prime }-x&=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }&=2 x+3 y+{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✗	0.340
4349	14731	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (3 x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.340
4350	14792	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.340
4351	16162	\begin{align*} y^{\prime }&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	0.340
4352	16169	\begin{align*} 1&=\left (x^{2}-9\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.340
4353	19243	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.340
4354	23612	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.340
4355	24776	\begin{align*} x {y^{\prime }}^{2}-2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.340
4356	421	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4357	4587	\begin{align*} y^{\prime \prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4358	6377	\begin{align*} b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✗	✗	✗	0.341
4359	6779	\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4360	7460	\begin{align*} y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4361	7821	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.341
4362	9367	\begin{align*} y^{\prime }&=1+y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4363	10355	\begin{align*} y^{\prime }+\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.341
4364	10579	\begin{align*} 3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.341
4365	14059	\begin{align*} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\ \end{align*}	✓	✓	✗	✗	0.341
4366	14378	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+2 y \\ \end{align*}	✓	✓	✓	✓	0.341
4367	15743	\(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.341
4368	16363	\begin{align*} \left (2+x \right ) y^{\prime }-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.341
4369	16829	\begin{align*} \left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.341
4370	18647	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.341
4371	428	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.342
4372	549	\begin{align*} x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
4373	1362	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.342
4374	3930	\begin{align*} y^{\prime }+2 y&=4 t \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
4375	6853	\begin{align*} n \cos \left (x n +m y\right )-m \sin \left (x m +n y\right )+\left (m \cos \left (x n +m y\right )-n \sin \left (x m +n y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.342
4376	6867	\begin{align*} y+\left (-x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4377	8849	\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.342
4378	8851	\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.342
4379	9031	\begin{align*} \cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4380	9044	\begin{align*} y_{1}^{\prime }&=y_{1} \\ y_{2}^{\prime }&=y_{1}+y_{2} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.342
4381	12905	\begin{align*} 2 y+a y^{3}+9 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	0.342
4382	14739	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y x&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.342
4383	15473	\begin{align*} x^{\prime }&=x \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.342
4384	16020	\begin{align*} x^{\prime }&=-3 x+10 y \\ y^{\prime }&=-x+3 y \\ \end{align*}	✓	✓	✓	✓	0.342
4385	16179	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.342
4386	18696	\begin{align*} x^{\prime }&=-x \\ y^{\prime }&=-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.342
4387	18884	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.342
4388	21857	\begin{align*} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	0.342
4389	22834	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x={\frac {1}{2}}\).	✓	✓	✓	✓	0.342
4390	548	\begin{align*} x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= -13 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.343
4391	1524	\begin{align*} y^{\prime }&=-x \\ \end{align*}	✓	✓	✓	✓	0.343
4392	2151	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&={\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \\ \end{align*}	✓	✓	✓	✓	0.343
4393	2827	\begin{align*} x_{1}^{\prime }&=-4 x_{1}-x_{2} \\ x_{2}^{\prime }&=x_{1}-6 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.343
4394	3722	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.343
4395	6696	\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x \left (x^{2}+3\right ) \\ \end{align*}	✓	✓	✓	✓	0.343
4396	6957	\begin{align*} y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
4397	7631	\begin{align*} y^{\prime }+\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.343
4398	7886	\begin{align*} 2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.343
4399	8027	\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }&=x +\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.343
4400	9065	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.343