2.3.156 Problems 15501 to 15600

Table 2.885: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15501	23160	\begin{align*} {\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.945
15502	15030	\begin{align*} x&={y^{\prime }}^{3}-y^{\prime }+2 \\ \end{align*}	✓	✓	✓	✓	1.946
15503	17387	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.946
15504	18723	\begin{align*} y^{\prime \prime }-y t&=\frac {1}{\pi } \\ \end{align*}	✓	✓	✓	✓	1.946
15505	1208	\begin{align*} y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.947
15506	27356	\begin{align*} {y^{\prime }}^{2} x&=y \\ \end{align*}	✓	✓	✓	✓	1.947
15507	8117	\begin{align*} y^{\prime }+y x&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	1.948
15508	13037	\begin{align*} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x}&=0 \\ \end{align*}	✗	✗	✗	✗	1.948
15509	14667	\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }&=x^{3}+x^{2} {\mathrm e}^{-x}+\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.948
15510	25558	\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.949
15511	14326	\begin{align*} t^{2} x^{\prime \prime }+3 x^{\prime } t -8 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.950
15512	1157	\begin{align*} y^{\prime }&=\frac {b +a y}{d +c y} \\ \end{align*}	✓	✓	✓	✓	1.951
15513	3309	\begin{align*} x&=y-{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	1.951
15514	6111	\begin{align*} -6 y-2 \left (1-2 x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.951
15515	6140	\begin{align*} -4 y+y^{\prime }+2 x \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.951
15516	22104	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.951
15517	27282	\begin{align*} x y^{\prime }+2 y+x^{5} y^{3} {\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.951
15518	6285	\begin{align*} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.952
15519	16479	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.953
15520	73	\begin{align*} y^{\prime }+y&=2 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.954
15521	6148	\begin{align*} 4 y+2 \left (1-2 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.954
15522	17357	\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -22 \\ \end{align*}	✓	✓	✓	✓	1.954
15523	24569	\begin{align*} 4 y^{\prime \prime }+y&=2 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.954
15524	25572	\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\sqrt {\frac {k}{m}}\, t \right ) \\ \end{align*}	✓	✓	✓	✓	1.954
15525	26469	\begin{align*} 1+{y^{\prime }}^{2}&=2 y y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✗	1.954
15526	23115	\begin{align*} y y^{\prime }-y^{2}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.955
15527	23384	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.955
15528	17386	\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.956
15529	1172	\begin{align*} y^{\prime }&=\frac {t^{2}+1}{3 y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	1.957
15530	9655	\begin{align*} x^{\prime }&=4 x-7 y \\ y^{\prime }&=5 x \\ \end{align*}	✓	✓	✓	✓	1.957
15531	14319	\begin{align*} x^{\prime \prime }+w^{2} x&=\cos \left (\beta t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.957
15532	20701	\begin{align*} y^{\prime \prime }+n^{2} y&=\sec \left (n x \right ) \\ \end{align*}	✓	✓	✓	✓	1.957
15533	21875	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.957
15534	7508	\begin{align*} y^{\prime }&=\sin \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	1.958
15535	27497	\begin{align*} x y^{\prime }&=x^{2} {\mathrm e}^{-y}+2 \\ \end{align*}	✓	✓	✓	✗	1.958
15536	2301	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	1.959
15537	3966	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.959
15538	6213	\begin{align*} -\left (x^{2}+4 x +2\right ) y-\left (-x^{3}-3 x^{2}+2 x +2\right ) y^{\prime }+x \left (-x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.959
15539	12342	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-y \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.959
15540	25582	\begin{align*} y^{\prime \prime }+2 p y^{\prime }+\omega _{n}^{2} y&=\omega _{n}^{2} t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.960
15541	27284	\begin{align*} y^{\prime } x^{3} \sin \left (y\right )&=x y^{\prime }-2 y \\ \end{align*}	✓	✓	✓	✓	1.960
15542	6033	\begin{align*} -\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.961
15543	15717	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.961
15544	6252	\begin{align*} \left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.962
15545	6219	\begin{align*} \left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+x^{2} \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.963
15546	999	\begin{align*} x_{1}^{\prime }&=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\ x_{3}^{\prime }&=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\ x_{4}^{\prime }&=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \\ \end{align*}	✓	✓	✓	✓	1.964
15547	5710	\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.964
15548	9938	\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.964
15549	21016	\begin{align*} x^{\prime }&=x+2 t \\ \end{align*}	✓	✓	✓	✓	1.964
15550	23151	\begin{align*} x y^{\prime }+y&=3 \\ \end{align*}	✓	✓	✓	✓	1.964
15551	22211	\begin{align*} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.965
15552	26894	\begin{align*} {\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}-1\right ) y^{\prime }&=0 \\ y \left (5\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.965
15553	2484	\begin{align*} y^{\prime }-2 y t&=1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.966
15554	9391	\begin{align*} x^{3} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.966
15555	15450	\begin{align*} y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.966
15556	206	\begin{align*} x y^{\prime }+y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.967
15557	1240	\begin{align*} \left (t +1\right ) y+t y^{\prime }&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	1.967
15558	15748	\begin{align*} y_{1}^{\prime }&=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }&=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	1.967
15559	15854	\begin{align*} y^{\prime }&=y \left (-1+y\right ) \left (y-3\right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✗	✗	1.967
15560	16749	\begin{align*} -y^{\prime }+x y^{\prime \prime }&=-3 x {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	1.968
15561	21554	\begin{align*} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=6 \left (x^{2}+1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.968
15562	26097	\begin{align*} y^{\prime \prime }&=18 y^{3} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	1.968
15563	3550	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \\ \end{align*}	✓	✓	✓	✗	1.969
15564	12645	\begin{align*} y^{\prime \prime }&=\frac {c y}{\left (x -a \right )^{2} \left (x -b \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.969
15565	13790	\begin{align*} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.969
15566	15408	\begin{align*} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.969
15567	15897	\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.969
15568	22750	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.969
15569	15933	\begin{align*} y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	1.970
15570	16552	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.970
15571	23326	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.970
15572	10030	\begin{align*} y&={y^{\prime }}^{2} x \\ \end{align*}	✓	✓	✓	✓	1.971
15573	12187	\begin{align*} y^{\prime }&=\frac {-2 x \cos \left (x \right )+2 x^{2} \sin \left (x \right )+2 x +2 y^{2}+4 y \cos \left (x \right ) x -4 y x +x^{2} \cos \left (2 x \right )+3 x^{2}-4 x^{2} \cos \left (x \right )}{2 x} \\ \end{align*}	✓	✓	✓	✓	1.971
15574	18630	\begin{align*} x^{\prime }&=x+2 y+\sin \left (t \right ) \\ y^{\prime }&=-x+y-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.971
15575	22709	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	1.971
15576	11834	\begin{align*} {y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.972
15577	24149	\begin{align*} v v^{\prime }&=g \\ v \left (x_{0} \right ) &= v_{0} \\ \end{align*}	✓	✗	✓	✓	1.972
15578	7025	\begin{align*} \left (1+x^{2}+y^{2}\right ) y^{\prime }+2 y x +x^{2}+3&=0 \\ \end{align*}	✓	✓	✓	✗	1.973
15579	15245	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.973
15580	19206	\begin{align*} x y^{\prime \prime }-y^{\prime }-x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.973
15581	24393	\begin{align*} y^{\prime }&=x -y+2 \\ \end{align*}	✓	✓	✓	✓	1.973
15582	25969	\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.973
15583	7505	\begin{align*} y^{\prime }&=\sqrt {x +y}-1 \\ \end{align*}	✓	✓	✓	✓	1.974
15584	13415	\begin{align*} y^{\prime }&=y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	1.974
15585	14745	\begin{align*} \left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.974
15586	26176	\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	1.974
15587	27465	\begin{align*} 2 y^{\prime }&=x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	1.974
15588	25	\begin{align*} y^{\prime }&=x^{2}-y \\ \end{align*}	✓	✓	✓	✓	1.975
15589	3627	\begin{align*} y-{\mathrm e}^{x}+y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.975
15590	10127	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.975
15591	17175	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	1.975
15592	21256	\begin{align*} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.976
15593	5533	\begin{align*} 4 x \left (-x +a \right ) \left (-x +b \right ) {y^{\prime }}^{2}&=\left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.977
15594	2474	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	1.978
15595	16490	\begin{align*} y^{\prime \prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.978
15596	18286	\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \\ y \left (\infty \right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✓	1.978
15597	24946	\begin{align*} y^{\prime }&=y-t \\ \end{align*}	✓	✓	✓	✓	1.978
15598	6159	\begin{align*} -\left (a^{2} x^{2}+1\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.979
15599	16569	\begin{align*} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.979
15600	69	\begin{align*} y^{\prime }&=y^{2} \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✓	1.980