2.3.131 Problems 13001 to 13100

Table 2.793: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13001	9344	\begin{align*} y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.296
13002	22549	\begin{align*} \left (\sin \left (y\right )-x \right ) y^{\prime }&=2 x +y \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	2.297
13003	75	\begin{align*} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.298
13004	3013	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.298
13005	5293	\begin{align*} \left (a +x^{2}+y^{2}\right ) y y^{\prime }&=x \left (a -x^{2}-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	2.298
13006	9785	\begin{align*} y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.298
13007	15015	\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.299
13008	9635	\begin{align*} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.300
13009	20567	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.300
13010	4093	\begin{align*} x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.302
13011	14146	\begin{align*} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	2.302
13012	13348	\begin{align*} y^{\prime } x&=a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2} \\ \end{align*}	✓	✓	✓	✗	2.303
13013	15661	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.303
13014	24351	\begin{align*} x -y+2+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.305
13015	81	\begin{align*} -y+y^{\prime } x&=x \\ y \left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	2.306
13016	4430	\begin{align*} 2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.306
13017	21729	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 4 \\ y \left (\pi \right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	2.306
13018	98	\begin{align*} \frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\ \end{align*}	✓	✓	✓	✓	2.307
13019	120	\begin{align*} y^{\prime }&=\sqrt {x +y+1} \\ \end{align*}	✓	✓	✓	✓	2.307
13020	756	\begin{align*} x \,{\mathrm e}^{y} y^{\prime }&=2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	2.307
13021	7745	\begin{align*} y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.307
13022	14162	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.307
13023	14327	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.307
13024	16345	\begin{align*} 2+2 x^{2}-2 y x +\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.307
13025	20038	\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.307
13026	20569	\begin{align*} a y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.307
13027	9195	\begin{align*} \sec \left (x \right ) y^{\prime }&=\sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.308
13028	17016	\begin{align*} y^{\prime }-y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.308
13029	10	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.309
13030	15583	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}+y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.309
13031	68	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	2.310
13032	710	\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ \end{align*}	✓	✓	✓	✓	2.310
13033	2978	\begin{align*} 2 y-y x -3+y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.310
13034	7431	\begin{align*} y^{\prime } x +3 y+3 x^{2}&=\frac {\sin \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	2.310
13035	16225	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.310
13036	4625	\begin{align*} y^{\prime }&=\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.311
13037	7800	\begin{align*} y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\ \end{align*}	✓	✓	✓	✓	2.311
13038	23185	\begin{align*} \cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.311
13039	783	\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\ \end{align*}	✗	✗	✗	✗	2.312
13040	15139	\begin{align*} x^{2} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.313
13041	15292	\begin{align*} x^{\prime }&=2 x+y-z+5 \sin \left (t \right ) \\ y^{\prime }&=y+z-10 \cos \left (t \right ) \\ z^{\prime }&=x+z+2 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.313
13042	23369	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.313
13043	12019	\begin{align*} y^{\prime }&=\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y} \\ \end{align*}	✓	✓	✓	✗	2.314
13044	15050	\begin{align*} x^{\prime }-x \cot \left (t \right )&=4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.314
13045	16381	\begin{align*} x^{2} y^{\prime }+3 y x&=6 \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.314
13046	7359	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}+4&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.315
13047	8391	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✗	✓	2.316
13048	8904	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.316
13049	7223	\begin{align*} y y^{\prime }+x y^{2}-8 x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.317
13050	9846	\begin{align*} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.317
13051	4642	\begin{align*} y^{\prime }&=\sin \left (2 x \right )+\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.318
13052	7537	\begin{align*} x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\ \end{align*}	✓	✓	✓	✓	2.318
13053	13930	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.318
13054	19381	\begin{align*} y+x^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	2.319
13055	24851	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	2.319
13056	3706	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.320
13057	8374	\begin{align*} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.320
13058	10364	\begin{align*} a {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.320
13059	20535	\begin{align*} y^{\prime \prime }&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.321
13060	21364	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	2.321
13061	12680	\begin{align*} y^{\prime \prime }&=-\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}-y \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.322
13062	5612	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.323
13063	14210	\begin{align*} x^{\prime }+t x^{\prime \prime }&=1 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.323
13064	15531	\begin{align*} y^{\prime }&=-y x \\ \end{align*}	✓	✓	✓	✓	2.323
13065	15606	\begin{align*} x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.323
13066	777	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.324
13067	1264	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.324
13068	18075	\begin{align*} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.324
13069	24997	\begin{align*} y^{\prime } t +2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.324
13070	8117	\begin{align*} y^{\prime }+y x&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	2.325
13071	12687	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+n \left (n -1\right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.325
13072	15799	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.325
13073	20223	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\ \end{align*}	✓	✓	✓	✓	2.325
13074	9636	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.326
13075	12319	\begin{align*} -a y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.326
13076	19344	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.326
13077	22440	\begin{align*} y^{3}+2 \,{\mathrm e}^{x} y+\left ({\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.326
13078	18555	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.327
13079	9008	\begin{align*} y^{\prime }&=\frac {x^{2}+x}{y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.328
13080	11449	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.328
13081	15920	\begin{align*} y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.328
13082	2492	\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.329
13083	17054	\begin{align*} t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.329
13084	19968	\begin{align*} y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	2.329
13085	13038	\begin{align*} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.330
13086	6806	\begin{align*} {y^{\prime }}^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✗	2.331
13087	12419	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.331
13088	707	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.332
13089	4610	\begin{align*} y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	2.332
13090	8425	\begin{align*} y^{\prime }+2 y x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	2.332
13091	9053	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.332
13092	16365	\begin{align*} y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.332
13093	8545	\begin{align*} y^{\prime \prime } x +3 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.333
13094	14516	\begin{align*} y^{\prime }&=-y^{2}+y x +1 \\ \end{align*}	✓	✓	✓	✗	2.333
13095	22075	\begin{align*} y^{\prime }+y x&=6 x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	2.333
13096	21414	\begin{align*} y^{\prime }+\frac {y}{y^{2} x^{2}+x}&=\frac {x y^{2}}{y^{2} x^{2}+x} \\ \end{align*}	✓	✓	✓	✗	2.334
13097	5962	\begin{align*} -\left (-a^{2} x^{2}+6\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.336
13098	15607	\begin{align*} \left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.336
13099	22606	\begin{align*} y^{\prime }+y x&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	2.336
13100	18266	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\left (12 x -7\right ) {\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.337