2.3.86 Problems 8501 to 8600

Table 2.721: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8501	14276	\begin{align*} x+3 t x^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.623
8502	14684	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}	✓	✓	✓	✗	0.623
8503	16065	\begin{align*} x^{\prime }&=-3 x-3 y \\ y^{\prime }&=2 x+y \\ \end{align*}	✓	✓	✓	✓	0.623
8504	18412	\begin{align*} x^{\prime }+3 x+4 y&=0 \\ y^{\prime }+2 x+5 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.623
8505	19516	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.623
8506	21138	\begin{align*} x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.623
8507	2584	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.624
8508	3742	\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.624
8509	9343	\begin{align*} y^{\prime \prime }+9 y&=-3 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.624
8510	12897	\begin{align*} x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\ \end{align*}	✗	✗	✗	✗	0.624
8511	14618	\begin{align*} y^{\prime \prime }-3 y^{\prime }+8 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.624
8512	15164	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.624
8513	17451	\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=-2 t^{3} {\mathrm e}^{4 t} \\ \end{align*}	✓	✓	✓	✓	0.624
8514	18907	\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.624
8515	21150	\begin{align*} x^{\prime \prime }+4 x&=\sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.624
8516	21246	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=-2 x-y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.624
8517	1921	\begin{align*} \left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.625
8518	4515	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.625
8519	5647	\begin{align*} {y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.625
8520	7730	\begin{align*} y^{\prime }-2 \tan \left (x \right ) y&=y^{2} \tan \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.625
8521	7759	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.625
8522	8538	\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.625
8523	9703	\begin{align*} x^{\prime }&=4 x-5 y \\ y^{\prime }&=5 x-4 y \\ \end{align*}	✓	✓	✓	✓	0.625
8524	13065	\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=2 x+2 y \\ \end{align*}	✓	✓	✓	✓	0.625
8525	13150	\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 2 & -2 & -1 \\ -2 & 6 & 3 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.625
8526	13673	\begin{align*} y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.625
8527	13933	\begin{align*} y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.625
8528	14624	\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.625
8529	18665	\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.625
8530	18904	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.625
8531	19589	\begin{align*} n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.625
8532	20421	\begin{align*} y&=y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	0.625
8533	21498	\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.625
8534	21523	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.625
8535	22152	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\ \end{align*}	✓	✓	✓	✓	0.625
8536	22945	\begin{align*} x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\ y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.625
8537	23101	\begin{align*} y^{\prime \prime } x +y&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	0.625
8538	23530	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	0.625
8539	24259	\begin{align*} \left (a +x \right ) y^{\prime }&=b x \\ \end{align*}	✓	✓	✓	✓	0.625
8540	24659	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=15 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.625
8541	24708	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.625
8542	24870	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.625
8543	25595	\begin{align*} y^{\prime \prime }+3 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.625
8544	25953	\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.625
8545	25981	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.625
8546	26109	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	0.625
8547	26512	\begin{align*} y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	0.625
8548	3292	\begin{align*} {y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.626
8549	3994	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.626
8550	7089	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.626
8551	7362	\begin{align*} y^{\prime }&=3 x^{2} y \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.626
8552	10523	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.626
8553	12427	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (a +x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.626
8554	16587	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.626
8555	16644	\begin{align*} y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.626
8556	18183	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=-2 \\ \end{align*}	✓	✓	✓	✓	0.626
8557	18259	\begin{align*} -4 y^{\prime }+y^{\prime \prime \prime }&=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.626
8558	18686	\begin{align*} x^{\prime }&=-\frac {3 x}{2}+y \\ y^{\prime }&=-\frac {x}{4}-\frac {y}{2} \\ \end{align*}	✓	✓	✓	✓	0.626
8559	23677	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +p^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.626
8560	24627	\begin{align*} y^{\prime \prime }-9 y&=18 x -162 x \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.626
8561	25817	\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.626
8562	3694	\begin{align*} \sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.627
8563	3728	\begin{align*} y^{\prime \prime }-4 y^{\prime }+6 y&=7 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.627
8564	3796	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.627
8565	6463	\begin{align*} -y^{\prime }+{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.627
8566	6502	\begin{align*} x y y^{\prime \prime }&=x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2} \\ \end{align*}	✗	✗	✗	✗	0.627
8567	15707	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x +\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.627
8568	17720	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.627
8569	21103	\begin{align*} x^{\prime }&=a y \\ y^{\prime }&=-a x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.627
8570	1917	\begin{align*} \left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.628
8571	5895	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.628
8572	6393	\begin{align*} x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.628
8573	7076	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{i x} \\ \end{align*}	✓	✓	✓	✓	0.628
8574	7795	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.628
8575	11677	\begin{align*} {y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.628
8576	14110	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x}-\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.628
8577	14736	\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.628
8578	15769	\begin{align*} x^{\prime }&=-x-2 y \\ y^{\prime }&=5 x+y \\ \end{align*}	✓	✓	✓	✓	0.628
8579	18660	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.628
8580	23449	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime }-y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.628
8581	23597	\begin{align*} c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}} \\ c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}} \\ \end{align*}	✓	✓	✓	✓	0.628
8582	641	\begin{align*} x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.629
8583	1024	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }&=-27 x_{1}-9 x_{2}-5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.629
8584	3391	\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{2}-x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.629
8585	6230	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.629
8586	7278	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.629
8587	7771	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=x^{2}-1 \\ \end{align*}	✓	✓	✓	✓	0.629
8588	8011	\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \\ \end{align*}	✓	✓	✓	✓	0.629
8589	9512	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.629
8590	14872	\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \\ \end{align*}	✓	✓	✓	✓	0.629
8591	16764	\begin{align*} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.629
8592	17117	\begin{align*} y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.629
8593	17590	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \tan \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.629
8594	17697	\begin{align*} y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.629
8595	22148	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\ \end{align*}	✓	✓	✓	✓	0.629
8596	22482	\begin{align*} x^{2} y^{\prime \prime }&=x^{2}+1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.629
8597	24539	\begin{align*} 4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x \\ \end{align*}	✓	✓	✓	✓	0.629
8598	25960	\begin{align*} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.629
8599	6385	\begin{align*} \left (-y+a x y^{\prime }\right )^{2}+y^{\prime \prime } x&=b \\ \end{align*}	✗	✗	✗	✗	0.630
8600	8905	\begin{align*} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.630