2.3.85 Problems 8401 to 8500

Table 2.719: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
8401	10293	\begin{align*} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.616
8402	16753	\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=123 x \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.616
8403	18210	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.616
8404	23681	\begin{align*} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.616
8405	23684	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.616
8406	24790	\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*}	✓	✓	✓	✓	0.616
8407	5393	\begin{align*} {y^{\prime }}^{2}+\left (a +x \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	0.617
8408	7596	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= {\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	0.617
8409	8478	\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.617
8410	8793	\begin{align*} s^{\prime \prime }+2 s^{\prime }+s&=0 \\ s \left (0\right ) &= 4 \\ s^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	0.617
8411	9983	\begin{align*} x^{\prime }&=-2 x+3 y \\ y^{\prime }&=-2 x+5 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -2 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.617
8412	12903	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.617
8413	19125	\begin{align*} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	0.617
8414	19515	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}	✓	✓	✓	✗	0.617
8415	3	\begin{align*} y^{\prime }&=\sqrt {x} \\ y \left (4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.618
8416	3422	\begin{align*} y^{\prime }&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.618
8417	4516	\begin{align*} y^{\prime \prime }+4 y&=8 \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.618
8418	7572	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.618
8419	9251	\begin{align*} y^{\prime \prime }+y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.618
8420	15093	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \\ \end{align*}	✓	✓	✓	✗	0.618
8421	16871	\begin{align*} y^{\prime \prime }+y \ln \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	0.618
8422	17408	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.618
8423	17752	\begin{align*} y^{\prime \prime }-9 y&=\frac {1}{1+{\mathrm e}^{3 t}} \\ \end{align*}	✓	✓	✓	✓	0.618
8424	18228	\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.618
8425	18859	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.618
8426	19054	\begin{align*} x_{1}^{\prime }&=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }&=-2 x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.618
8427	19873	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	0.618
8428	21493	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.618
8429	22204	\begin{align*} 3 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.618
8430	22916	\begin{align*} x^{\prime }+3 x+2 y&=0 \\ 3 x+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.618
8431	23793	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.618
8432	23820	\begin{align*} x^{\prime }&=x+y \\ y^{\prime }&=x-3 y \\ \end{align*}	✓	✓	✓	✓	0.618
8433	24747	\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.618
8434	501	\begin{align*} 5 y^{\prime \prime } x +\left (30+3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.619
8435	6937	\begin{align*} y \sec \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.619
8436	8549	\begin{align*} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.619
8437	11668	\begin{align*} {y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \\ \end{align*}	✓	✓	✓	✓	0.619
8438	14602	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	0.619
8439	14634	\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 x^{2}+4 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.619
8440	16610	\begin{align*} y^{\prime \prime }+9 y&=10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.619
8441	17430	\begin{align*} y^{\prime \prime }+y&=\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.619
8442	24548	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=50 x +13 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.619
8443	24581	\begin{align*} y^{\prime \prime }+9 y&=18 x -3+20 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.619
8444	25313	\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.619
8445	598	\begin{align*} x^{\prime }&=x+2 y+z \\ y^{\prime }&=6 x-y \\ z^{\prime }&=-x-2 y-z \\ \end{align*}	✓	✓	✓	✓	0.620
8446	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*}	✓	✓	✓	✓	0.620
8447	1035	\begin{align*} x_{1}^{\prime }&=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }&=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }&=17 x_{1}+7 x_{2}+5 x_{3} \\ \end{align*}	✓	✓	✓	✓	0.620
8448	1433	\begin{align*} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}+\frac {1}{t} \\ x_{2}^{\prime }&=2 x_{1}-x_{2}+\frac {2}{t}+4 \\ \end{align*}	✓	✓	✓	✓	0.620
8449	2000	\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.620
8450	2403	\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	0.620
8451	4519	\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.620
8452	9378	\begin{align*} y^{\prime \prime }+y^{\prime }-y x&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.620
8453	9632	\begin{align*} -y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.620
8454	13188	\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.620
8455	16393	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.620
8456	21648	\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.620
8457	25194	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=2 t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	0.620
8458	502	\begin{align*} y^{\prime \prime } x -\left (x +4\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	0.621
8459	2744	\begin{align*} x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }&=4 x_{1}-x_{2} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	0.621
8460	3484	\begin{align*} f^{\prime \prime }+2 f^{\prime }+5 f&=0 \\ f \left (0\right ) &= 1 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.621
8461	3898	\begin{align*} x_{1}^{\prime }&=3 x_{1}+13 x_{2} \\ x_{2}^{\prime }&=-x_{1}-3 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.621
8462	6721	\begin{align*} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.621
8463	12957	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4}&=0 \\ \end{align*}	✗	✗	✗	✗	0.621
8464	14351	\begin{align*} x^{\prime }+5 x&=\operatorname {Heaviside}\left (-2+t \right ) \\ x \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.621
8465	20416	\begin{align*} y&=y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	0.621
8466	23535	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	0.621
8467	26134	\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=-5 x-y \\ \end{align*}	✓	✓	✓	✓	0.621
8468	835	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.622
8469	917	\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.622
8470	3423	\begin{align*} y^{\prime }&=\frac {t}{\sqrt {t}+1} \\ \end{align*}	✓	✓	✓	✓	0.622
8471	9592	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622
8472	12369	\begin{align*} y^{\prime \prime } x -2 y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	0.622
8473	14306	\begin{align*} x^{\prime \prime }+x^{\prime }+x&=-6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.622
8474	14403	\begin{align*} x^{\prime }&=3 x-2 y \\ y^{\prime }&=4 x-y \\ \end{align*}	✓	✓	✓	✓	0.622
8475	14560	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.622
8476	14925	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.622
8477	16589	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	0.622
8478	16969	\begin{align*} x^{\prime \prime }+x&=t \cos \left (t \right )-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.622
8479	17445	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=25 \sin \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	0.622
8480	17687	\begin{align*} \left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622
8481	17721	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.622
8482	18908	\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 1 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.622
8483	19577	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.622
8484	19661	\begin{align*} x^{\prime }&=\frac {1}{t^{2}+1} \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.622
8485	20179	\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.622
8486	20927	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-3 x \\ \end{align*}	✓	✓	✓	✓	0.622
8487	21113	\begin{align*} 4 x^{\prime }+2 x^{\prime \prime }&=-5 x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.622
8488	21209	\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=-3 x+y \\ \end{align*}	✓	✓	✓	✓	0.622
8489	21213	\begin{align*} x^{\prime }&=3 x+t \\ y^{\prime }&=-y+2 t \\ \end{align*}	✓	✓	✓	✓	0.622
8490	21591	\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.622
8491	22166	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.622
8492	22702	\begin{align*} 4 y+y^{\prime \prime }&=8 \cos \left (2 x \right )-4 x \\ \end{align*}	✓	✓	✓	✓	0.622
8493	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 \(x=0\).	✓	✓	✓	✓	0.623
8494	2583	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	0.623
8495	4001	\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.623
8496	6017	\begin{align*} \left (a \left (1+a \right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.623
8497	6932	\begin{align*} 4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.623
8498	7522	\begin{align*} y^{\prime }&=-4 x-y \\ x^{\prime }&=2 x-y \\ \end{align*}	✓	✓	✓	✓	0.623
8499	9273	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.623
8500	11288	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.623