2.3.58 Problems 5701 to 5800

Table 2.659: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5701	13998	\begin{align*} y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.370
5702	15705	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.370
5703	18653	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\ \end{align*}	✓	✓	✓	✓	0.370
5704	19660	\begin{align*} x^{\prime }&=b \,{\mathrm e}^{t} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.370
5705	21514	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.370
5706	21523	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.370
5707	24544	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=6 x +6 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.370
5708	24599	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.370
5709	898	\begin{align*} y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.371
5710	1315	\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+82 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.371
5711	1682	\begin{align*} 14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
5712	2415	\begin{align*} y^{\prime \prime }-y t^{3}&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.371
5713	2550	\begin{align*} 5 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.371
5714	3124	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.371
5715	3812	\begin{align*} x_{1}^{\prime }&=2 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-4 x_{1}-6 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.371
5716	7947	\begin{align*} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.371
5717	10383	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	0.371
5718	11006	\begin{align*} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.371
5719	11669	\begin{align*} {y^{\prime }}^{2}+\left (a +x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.371
5720	12849	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \\ \end{align*}	✗	✗	✗	✗	0.371
5721	18891	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=t \cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.371
5722	19559	\begin{align*} 4 y^{\prime \prime }+y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.371
5723	20346	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{\frac {5 x}{2}} \\ \end{align*}	✓	✓	✓	✓	0.371
5724	21581	\begin{align*} y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.371
5725	22234	\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.371
5726	24105	\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{3}+x \right ) y^{\prime }-x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371
5727	884	\begin{align*} 4 y+y^{\prime \prime }&=2 x \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.372
5728	3263	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
5729	3276	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.372
5730	3569	\begin{align*} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
5731	3884	\begin{align*} x_{1}^{\prime }&=3 x_{1}-x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.372
5732	4002	\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372
5733	9177	\begin{align*} y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
5734	10521	\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.372
5735	14574	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.372
5736	21213	\begin{align*} x^{\prime }&=3 x+t \\ y^{\prime }&=-y+2 t \\ \end{align*}	✓	✓	✓	✓	0.372
5737	24642	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.372
5738	25113	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.372
5739	26071	\begin{align*} y^{\prime }&=-2 z \\ z^{\prime }&=y+2 z \\ \end{align*}	✓	✓	✓	✓	0.372
5740	7263	\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.373
5741	7906	\begin{align*} y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.373
5742	8134	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.373
5743	8148	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.373
5744	8941	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.373
5745	9170	\begin{align*} y^{\prime } x +y+3 x^{3} y^{4} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.373
5746	10337	\begin{align*} y^{\prime } t +y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.373
5747	13060	\begin{align*} x^{\prime }&=a y \\ y^{\prime }&=-a x \\ \end{align*}	✓	✓	✓	✓	0.373
5748	16785	\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.373
5749	20176	\begin{align*} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.373
5750	21865	\begin{align*} \left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.373
5751	22298	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.373
5752	24090	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.373
5753	3188	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.374
5754	6951	\begin{align*} y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.374
5755	7583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
5756	8485	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.374
5757	8584	\begin{align*} y^{\prime \prime }+\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.374
5758	10104	\begin{align*} y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✗	0.374
5759	18235	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
5760	21877	\begin{align*} 3 y^{\prime \prime }-4 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.374
5761	24549	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.374
5762	25059	\begin{align*} y^{\prime }-4 y&=1 \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.374
5763	25133	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 t} \\ \end{align*}	✓	✓	✓	✓	0.374
5764	374	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.375
5765	615	\begin{align*} x_{1}^{\prime }&=4 x_{1}-3 x_{2} \\ x_{2}^{\prime }&=6 x_{1}-7 x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 8 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
5766	817	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.375
5767	1335	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.375
5768	1447	\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.375
5769	2228	\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=x^{3} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	0.375
5770	2367	\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
5771	2672	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.375
5772	4130	\begin{align*} y^{\prime \prime }+y&=x^{3}+x \\ \end{align*}	✓	✓	✓	✓	0.375
5773	6079	\begin{align*} -\left (x^{2}+1\right ) y-4 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
5774	8714	\begin{align*} y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.375
5775	9028	\begin{align*} 2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.375
5776	9455	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.375
5777	18323	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )^{3}} \\ \end{align*}	✓	✓	✓	✓	0.375
5778	19635	\begin{align*} y^{\prime \prime }-y^{\prime }&=t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.375
5779	20166	\begin{align*} y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	0.375
5780	20663	\begin{align*} y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=\left (x -2\right ) {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	0.375
5781	20927	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-3 x \\ \end{align*}	✓	✓	✓	✓	0.375
5782	21572	\begin{align*} y^{\prime \prime }-y&=2 x +{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.375
5783	21580	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.375
5784	24019	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.375
5785	25617	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.375
5786	5366	\begin{align*} {y^{\prime }}^{2}&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.376
5787	5914	\begin{align*} -y-\left (-x +2\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	0.376
5788	7997	\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.376
5789	8132	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.376
5790	8909	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.376
5791	16995	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.376
5792	17834	\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
5793	18817	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.376
5794	20467	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.376
5795	21585	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.376
5796	21945	\begin{align*} y^{\prime \prime }+4 y&=2 t -8 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.376
5797	22643	\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.376
5798	24646	\begin{align*} 4 y+y^{\prime \prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.376
5799	4166	\begin{align*} y_{1}^{\prime }&=y_{1}+y_{2} \\ y_{2}^{\prime }&=3 y_{2}-y_{1} \\ \end{align*}	✓	✓	✓	✓	0.377
5800	7078	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.377