2.3.87 Problems 8601 to 8700

Table 2.747: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8601	16584	\begin{align*} 4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.632
8602	17426	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.632
8603	18382	\begin{align*} y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.632
8604	18984	\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.632
8605	20712	\begin{align*} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.632
8606	25126	\begin{align*} y^{\prime \prime }-8 y^{\prime }+25 y&=104 \sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.632
8607	27665	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.632
8608	2286	\begin{align*} y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.633
8609	2739	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }&=-x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	0.633
8610	8285	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.633
8611	16432	\begin{align*} y^{\prime \prime }&=2 y y^{\prime } \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	0.633
8612	22129	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.633
8613	46	\begin{align*} y^{\prime }&=3 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	0.634
8614	2285	\begin{align*} y_{1}^{\prime }&=-y_{1}+2 y_{2} \\ y_{2}^{\prime }&=-5 y_{1}+5 y_{2} \\ \end{align*}	✓	✓	✓	✓	0.634
8615	2713	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.634
8616	3486	\begin{align*} f^{\prime \prime }+6 f^{\prime }+9 f&={\mathrm e}^{-t} \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= \lambda \\ \end{align*}	✓	✓	✓	✓	0.634
8617	4152	\begin{align*} y^{\prime \prime }+2 y^{\prime }-2 y&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.634
8618	5427	\begin{align*} {y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	0.634
8619	8081	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.634
8620	8132	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.634
8621	12325	\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.634
8622	13104	\begin{align*} x^{\prime }&=y-z \\ y^{\prime }&=x+y \\ z^{\prime }&=x+z \\ \end{align*}	✓	✓	✓	✓	0.634
8623	16610	\begin{align*} y^{\prime \prime }+9 y&=10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.634
8624	24044	\begin{align*} x \left (x -1\right ) y^{\prime \prime }+\left (-x^{2}+2 x +1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.634
8625	24654	\begin{align*} y^{\prime \prime }+36 y&=\sin \left (6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.634
8626	26229	\begin{align*} \left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.634
8627	27109	\(\left [\begin {array}{ccc} 0 & 1 & 1 \\ 1 & 2 & 0 \\ 1 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.634
8628	881	\begin{align*} 4 y+y^{\prime \prime }&=3 x \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8629	883	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8630	1393	\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=2\).	✓	✓	✓	✓	0.635
8631	1809	\begin{align*} y^{\prime \prime }-y&=\frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \\ \end{align*}	✓	✓	✓	✓	0.635
8632	1918	\begin{align*} \left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.635
8633	2703	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.635
8634	3571	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.635
8635	8496	\begin{align*} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.635
8636	15159	\begin{align*} y^{\prime \prime }+\frac {k x}{y^{4}}&=0 \\ \end{align*}	✗	✓	✗	✗	0.635
8637	16671	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 x \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8638	18137	\begin{align*} y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.635
8639	18198	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \\ \end{align*}	✓	✓	✓	✓	0.635
8640	18472	\begin{align*} x^{\prime \prime }+x&=2 \cos \left (t \right ) \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.635
8641	18822	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.635
8642	20542	\begin{align*} x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8643	20853	\begin{align*} y^{\prime \prime }-y&=1+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.635
8644	20982	\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.635
8645	23515	\begin{align*} y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8646	23626	\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 5 \\ z \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.635
8647	24615	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=12 \,{\mathrm e}^{-2 x} x \\ \end{align*}	✓	✓	✓	✓	0.635
8648	24697	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8649	24734	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.635
8650	27136	\(\left [\begin {array}{ccc} -1 & 0 & 3-i \\ 0 & 1 & 0 \\ 3+i & 0 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.635
8651	1341	\begin{align*} y^{\prime \prime }+y&=2 \sec \left (\frac {t}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	0.636
8652	3149	\begin{align*} 4 y+y^{\prime \prime }&=2 x -2 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.636
8653	3319	\begin{align*} {y^{\prime }}^{3}+x y y^{\prime }&=2 y^{2} \\ \end{align*}	✓	✓	✓	✗	0.636
8654	7581	\begin{align*} y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	0.636
8655	8164	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.636
8656	9504	\begin{align*} 2 y-x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.636
8657	10465	\begin{align*} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.636
8658	15209	\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= -24 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.636
8659	15213	\begin{align*} 4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.636
8660	16643	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.636
8661	16873	\begin{align*} y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.636
8662	18018	\begin{align*} {y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	0.636
8663	21133	\begin{align*} x^{\prime \prime }+x&=3 t^{2}+t \\ \end{align*}	✓	✓	✓	✓	0.636
8664	21656	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.636
8665	24106	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (-x^{2}+9\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.636
8666	25115	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.636
8667	25122	\begin{align*} y^{\prime \prime }+y&=2 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.636
8668	3924	\begin{align*} x_{1}^{\prime }&=-3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=x_{1}-7 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.637
8669	8969	\begin{align*} y^{\prime \prime }+y \,{\mathrm e}^{x}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.637
8670	11777	\begin{align*} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.637
8671	14598	\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.637
8672	16121	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \cos \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.637
8673	17817	\begin{align*} x^{\prime \prime }+x&=\cos \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.637
8674	24745	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}	✓	✓	✓	✓	0.637
8675	24901	\begin{align*} x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.637
8676	349	\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=\left (x^{2}+1\right ) \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.638
8677	1034	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }&=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }&=8 x_{1}-8 x_{2}+10 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.638
8678	2755	\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*}	✓	✓	✓	✓	0.638
8679	2784	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{2} \\ x_{3}^{\prime }&=3 x_{3}+{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.638
8680	3290	\begin{align*} y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.638
8681	3862	\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\ \end{align*}	✓	✓	✓	✓	0.638
8682	5617	\begin{align*} {y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\ \end{align*}	✓	✓	✓	✓	0.638
8683	6603	\begin{align*} y^{\prime \prime \prime }&=\sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	0.638
8684	8113	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.638
8685	9248	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\ \end{align*}	✓	✓	✓	✓	0.638
8686	9368	\begin{align*} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.638
8687	10490	\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.638
8688	11389	\begin{align*} x y^{\prime }-\sqrt {a^{2}-x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.638
8689	14601	\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	0.638
8690	15208	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ y^{\prime \prime }\left (0\right ) &= -20 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.638
8691	15494	\begin{align*} x y^{\prime }-\sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	0.638
8692	17592	\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\tan \left (2 t \right )^{2} \\ \end{align*}	✓	✓	✓	✓	0.638
8693	18821	\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.638
8694	19226	\begin{align*} x^{\prime }+5 x+y&={\mathrm e}^{t} \\ y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	0.638
8695	19240	\begin{align*} 1+y^{2}+y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.638
8696	21114	\begin{align*} x^{\prime \prime }-6 x^{\prime }+9 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.638
8697	23493	\begin{align*} y^{\prime \prime }-y&=x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.638
8698	24570	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }-3 y&=-9 x^{2}-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.638
8699	25589	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.638
8700	25604	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	0.638