2.3.128 Problems 12701 to 12800

Table 2.805: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
12701	8423	\begin{align*} 3 y^{\prime }+12 y&=4 \\ \end{align*}	✓	✓	✓	✓	1.167
12702	8764	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.167
12703	16557	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.167
12704	18217	\begin{align*} y^{\prime \prime }+y&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.167
12705	18870	\begin{align*} y^{\prime \prime }+4 y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.167
12706	6004	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.168
12707	7911	\begin{align*} 3 y^{3}-y x -\left (x^{2}+6 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.168
12708	8987	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	1.168
12709	12378	\begin{align*} y^{\prime \prime } x -\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.168
12710	16724	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.168
12711	16749	\begin{align*} -y^{\prime }+y^{\prime \prime } x&=-3 {y^{\prime }}^{3} x \\ \end{align*}	✓	✓	✓	✓	1.168
12712	9826	\begin{align*} {y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	1.169
12713	9939	\begin{align*} y^{\prime \prime } x +y^{\prime }+\left (x +1\right ) x y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.169
12714	26472	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.169
12715	5841	\begin{align*} -a \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.170
12716	6314	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.170
12717	9185	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.170
12718	25933	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	1.170
12719	13030	\begin{align*} \left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }-b&=0 \\ \end{align*}	✗	✓	✓	✗	1.171
12720	14058	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	1.171
12721	18625	\begin{align*} y^{\prime } x&=-\frac {1}{\ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	1.171
12722	19874	\begin{align*} y^{\prime \prime } x +3 y^{\prime }&=3 x \\ \end{align*}	✓	✓	✓	✓	1.171
12723	16193	\begin{align*} y^{\prime } x&=\sin \left (x^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.172
12724	21738	\begin{align*} x^{\prime }&=2 x+2 y-z \\ y^{\prime }&=y+z \\ z^{\prime }&=z-y \\ \end{align*}	✓	✓	✓	✓	1.172
12725	24635	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=48 \,{\mathrm e}^{-x} \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.172
12726	10268	\begin{align*} y^{\prime }&=b y \\ \end{align*}	✓	✓	✓	✓	1.173
12727	74	\begin{align*} y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.174
12728	6566	\begin{align*} A y+\left (a +2 b x +c \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	1.174
12729	8407	\begin{align*} {y^{\prime }}^{2}+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	1.174
12730	12291	\begin{align*} y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.174
12731	14881	\begin{align*} x^{\prime }&=1-x \\ \end{align*}	✓	✓	✓	✓	1.174
12732	15177	\begin{align*} \left (\cos \left (y\right )-\sin \left (y\right ) y\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right )&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✗	✗	1.174
12733	20890	\begin{align*} y^{\prime \prime }-y^{\prime } x +3 y&=0 \\ y \left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.174
12734	22323	\begin{align*} y^{\prime }&={\mathrm e}^{y} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.174
12735	24628	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=4 x -6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.174
12736	3393	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y&=-2 x^{2}+x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.175
12737	9861	\begin{align*} -\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.175
12738	11385	\begin{align*} y^{\prime }-f \left (a x +b y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.175
12739	22275	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (1\right ) &= 0 \\ x_{2} \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.175
12740	2437	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.176
12741	1125	\begin{align*} \frac {2 y}{3}+y^{\prime }&=1-\frac {t}{2} \\ \end{align*}	✓	✓	✓	✓	1.177
12742	3165	\begin{align*} y^{\prime \prime }+y&=\tan \left (\frac {x}{3}\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.177
12743	4188	\begin{align*} y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x \left (x +1\right )}-\frac {y}{x \left (x +1\right )}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.177
12744	5969	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.177
12745	9405	\begin{align*} 4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.177
12746	17511	\begin{align*} y^{\prime \prime }+y&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	1.177
12747	19009	\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=-x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	1.177
12748	19041	\begin{align*} x_{1}^{\prime }&=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	1.177
12749	20903	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.177
12750	20986	\begin{align*} y^{\prime }&={\mathrm e}^{x}+x \cos \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.177
12751	23629	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ z^{\prime }&=x+y-5 z \\ u^{\prime }&=5 z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ z \left (0\right ) &= 0 \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.177
12752	13413	\begin{align*} y^{\prime }&=y^{2}-\tan \left (x \right ) y+a \left (1-a \right ) \cot \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.178
12753	14780	\begin{align*} x^{\prime }-y^{\prime }-2 x+4 y&=t \\ x^{\prime }+y^{\prime }-x-y&=1 \\ \end{align*}	✓	✓	✓	✓	1.178
12754	16570	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.178
12755	18332	\begin{align*} x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.178
12756	21693	\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✗	1.178
12757	4071	\begin{align*} 4 y^{\prime \prime } x +3 y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.179
12758	7311	\begin{align*} y^{\prime \prime }+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.179
12759	9439	\begin{align*} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=\infty \).	✓	✓	✓	✓	1.179
12760	15108	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.179
12761	20515	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }&=\left (3+2 x \right ) \left (4+2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.179
12762	244	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.180
12763	4602	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.180
12764	6496	\begin{align*} x {y^{\prime }}^{2}+x y y^{\prime \prime }&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.180
12765	24729	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.180
12766	3706	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.181
12767	5629	\begin{align*} {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.181
12768	6158	\begin{align*} -\left (\left (2 n +1\right )^{2}-4 x^{2}\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.181
12769	7914	\begin{align*} 2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.181
12770	15527	\begin{align*} y^{\prime }&=1+y \\ \end{align*}	✓	✓	✓	✓	1.181
12771	16559	\begin{align*} x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.181
12772	19851	\begin{align*} e y^{\prime \prime }&=-P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \\ \end{align*}	✓	✓	✓	✓	1.181
12773	25446	\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 i t} \\ \end{align*}	✓	✓	✓	✓	1.181
12774	3434	\begin{align*} y^{\prime }&=1-y \\ \end{align*}	✓	✓	✓	✓	1.182
12775	18116	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.182
12776	2765	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.183
12777	9740	\begin{align*} 2 {y^{\prime }}^{3} x -6 y {y^{\prime }}^{2}+x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.183
12778	9905	\begin{align*} x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.183
12779	12460	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.183
12780	8770	\begin{align*} 2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✗	1.184
12781	21225	\begin{align*} x^{\prime }&=x+3 y+2 t \\ y^{\prime }&=x-y+t^{2} \\ \end{align*}	✓	✓	✓	✓	1.184
12782	23051	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=7 \\ \end{align*}	✓	✓	✓	✓	1.184
12783	4013	\begin{align*} 4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.185
12784	85	\begin{align*} y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.186
12785	4570	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\ x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\ \end{align*}	✓	✓	✓	✓	1.186
12786	7903	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.186
12787	6142	\begin{align*} y+\left (1-x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.187
12788	11282	\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 \left (x -1\right ) x}\right ) y \\ \end{align*}	✓	✓	✓	✓	1.187
12789	15157	\begin{align*} \left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.187
12790	19230	\begin{align*} y^{\prime }&=k y \\ \end{align*}	✓	✓	✓	✓	1.187
12791	19430	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=6 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.187
12792	19504	\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}	✓	✓	✓	✓	1.187
12793	2628	\begin{align*} 2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.188
12794	5642	\begin{align*} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✗	✓	1.188
12795	15175	\begin{align*} y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.188
12796	18839	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.188
12797	19264	\begin{align*} \left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.188
12798	22276	\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.188
12799	25405	\begin{align*} y^{\prime }+9 y&=90 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.188
12800	3367	\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.189