2.3.94 Problems 9301 to 9400

Table 2.761: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
9301	524	\begin{align*} y^{\prime \prime }+x^{4} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.687
9302	525	\begin{align*} x y^{\prime \prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.687
9303	911	\begin{align*} x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 90 \\ \end{align*}	✓	✓	✓	✓	0.687
9304	3238	\begin{align*} x^{\prime }+2 x&=3 t \\ x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.687
9305	3254	\begin{align*} x^{2} y^{\prime \prime }&=x y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✓	0.687
9306	4131	\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.687
9307	4496	\begin{align*} y^{\prime \prime }-y&=\frac {1}{x}-\frac {2}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.687
9308	6937	\begin{align*} y \sec \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.687
9309	8579	\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.687
9310	9420	\begin{align*} y^{\prime \prime }-x y^{\prime }+y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.687
9311	10204	\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.687
9312	10247	\begin{align*} y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.687
9313	11753	\begin{align*} y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.687
9314	14792	\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.687
9315	15026	\begin{align*} {y^{\prime }}^{2}&=9 y^{4} \\ \end{align*}	✓	✓	✓	✓	0.687
9316	15093	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \\ \end{align*}	✓	✓	✓	✗	0.687
9317	18410	\begin{align*} x^{\prime }&=-9 y \\ y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	0.687
9318	18813	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.687
9319	19299	\begin{align*} \cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.687
9320	19984	\begin{align*} y^{2}+x y y^{\prime }-{y^{\prime }}^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.687
9321	20598	\begin{align*} {\mathrm e}^{x} \left (-y^{\prime }+x y^{\prime \prime }\right )&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.687
9322	22618	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.687
9323	23581	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= -{\frac {5}{18}} \\ x_{2} \left (0\right ) &= {\frac {47}{9}} \\ \end{align*}	✓	✓	✓	✓	0.687
9324	24662	\begin{align*} 4 y^{\prime \prime }-y&={\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.687
9325	25124	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 t \,{\mathrm e}^{-3 t} \\ \end{align*}	✓	✓	✓	✓	0.687
9326	486	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.688
9327	2055	\begin{align*} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.688
9328	3725	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.688
9329	3876	\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=-2 x_{1}-x_{2}+6 \,{\mathrm e}^{t} t \\ \end{align*}	✓	✓	✓	✓	0.688
9330	3909	\begin{align*} x_{1}^{\prime }&=7 x_{1}-2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=4 x_{2}-x_{3} \\ x_{3}^{\prime }&=-x_{1}+x_{2}+4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.688
9331	10172	\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\sin \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	0.688
9332	12324	\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	0.688
9333	17497	\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}	✓	✓	✓	✓	0.688
9334	18701	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-8 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.688
9335	15471	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=2 x-2 y \\ \end{align*}	✓	✓	✓	✓	0.689
9336	16691	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	0.689
9337	18457	\begin{align*} x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\ x \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.689
9338	480	\begin{align*} 3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.690
9339	2659	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.690
9340	3896	\begin{align*} x_{1}^{\prime }&=3 x_{1}+4 x_{3} \\ x_{2}^{\prime }&=2 x_{2} \\ x_{3}^{\prime }&=-4 x_{1}-5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.690
9341	3916	\begin{align*} x_{1}^{\prime }&=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \\ \end{align*}	✓	✓	✓	✓	0.690
9342	5789	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.690
9343	6306	\begin{align*} y^{\prime \prime }&=a -2 a b x y+2 y^{3} b^{2} \\ \end{align*}	✗	✗	✗	✗	0.690
9344	9524	\begin{align*} y^{\prime \prime }+5 x y^{\prime }+y \sqrt {x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✗	✗	0.690
9345	19039	\begin{align*} x_{1}^{\prime }&=-k_{1} x_{1} \\ x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }&=k_{2} x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= m_{0} \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.690
9346	20807	\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.690
9347	24626	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=4-8 x +6 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.690
9348	25941	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.690
9349	1027	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+x_{4} \\ x_{2}^{\prime }&=2 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{3}+x_{4} \\ x_{4}^{\prime }&=2 x_{4} \\ \end{align*}	✓	✓	✓	✓	0.691
9350	1431	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.691
9351	1750	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.691
9352	2033	\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.691
9353	3375	\begin{align*} x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.691
9354	4134	\begin{align*} y^{\prime \prime }-y&=2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.691
9355	8133	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.691
9356	10238	\begin{align*} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.691
9357	14924	\begin{align*} 2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= 9 \\ \end{align*}	✓	✓	✓	✓	0.691
9358	14957	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.691
9359	17787	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.691
9360	18700	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.691
9361	19149	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.691
9362	20189	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.691
9363	20208	\begin{align*} 4 x^{\prime }+9 y^{\prime }+44 x+49 y&=t \\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.691
9364	26598	\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+4 \sin \left (2 x \right ) \\ y \left (\pi \right ) &= 2 \pi \\ y^{\prime }\left (\pi \right ) &= 2 \pi \\ \end{align*}	✓	✓	✓	✓	0.691
9365	3899	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-10 x_{2} \\ x_{2}^{\prime }&=5 x_{1}+11 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.692
9366	7807	\begin{align*} x^{\prime \prime }+4 x&=\sin \left (2 t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.692
9367	10042	\begin{align*} y^{\prime \prime }&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.692
9368	12984	\begin{align*} x \left (x +y\right ) y^{\prime \prime }+{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	0.692
9369	14812	\begin{align*} y+y^{\prime }&=2 \sin \left (t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.692
9370	16590	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 12 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.692
9371	18321	\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	0.692
9372	3821	\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2}+t \\ x_{2}^{\prime }&=-2 x_{1}+x_{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.693
9373	8905	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.693
9374	17772	\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\frac {{\mathrm e}^{4 t}}{t^{3}} \\ \end{align*}	✓	✓	✓	✓	0.693
9375	19980	\begin{align*} y&=2 y^{\prime }+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.693
9376	21499	\begin{align*} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.693
9377	24716	\begin{align*} y^{\prime \prime }-y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.693
9378	24751	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	0.693
9379	1817	\begin{align*} 2 x y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (\sqrt {x}\right ) \\ \end{align*}	✓	✓	✓	✗	0.694
9380	2594	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=t \,{\mathrm e}^{\alpha t} \\ \end{align*}	✓	✓	✓	✓	0.694
9381	2706	\begin{align*} x^{\prime }&=3 x-4 y+{\mathrm e}^{t} \\ y^{\prime }&=x-y+{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.694
9382	2783	\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2}+4 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.694
9383	3372	\begin{align*} x y^{\prime \prime }+y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694
9384	9366	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694
9385	9799	\begin{align*} y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.694
9386	10356	\begin{align*} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✗	✗	0.694
9387	12545	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.694
9388	12660	\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \\ \end{align*}	✓	✓	✓	✗	0.694
9389	14381	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.694
9390	14853	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=3 x+y \\ \end{align*}	✓	✓	✓	✓	0.694
9391	16597	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.694
9392	18648	\begin{align*} x^{\prime }&=x-2 y \\ y^{\prime }&=3 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.694
9393	20752	\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\ \end{align*}	✓	✓	✓	✓	0.694
9394	20767	\begin{align*} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.694
9395	21887	\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.694
9396	22688	\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.694
9397	23729	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694
9398	27077	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694
9399	2444	\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y&=0 \\ \end{align*} Series expansion around \(t=-1\).	✗	✗	✓	✗	0.695
9400	2731	\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.695