2.3.196 Problems 19501 to 19600

Table 2.941: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19501	4859	\begin{align*} 2 \left (1-x \right ) y^{\prime }&=4 x \sqrt {1-x}+y \\ \end{align*}	✓	✓	✓	✓	4.460
19502	17072	\begin{align*} \frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.460
19503	4198	\begin{align*} y^{\prime } x -n y&=x^{n} \\ \end{align*}	✓	✓	✓	✓	4.461
19504	4342	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.461
19505	14459	\begin{align*} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.461
19506	17245	\begin{align*} 2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.461
19507	7940	\begin{align*} y^{\prime }+x \left (x +y\right )&=x^{3} \left (x +y\right )^{3}-1 \\ \end{align*}	✓	✓	✓	✓	4.462
19508	17984	\begin{align*} x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.462
19509	17006	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.463
19510	4871	\begin{align*} x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	4.466
19511	4635	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\ \end{align*}	✓	✓	✓	✗	4.467
19512	1595	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.468
19513	11417	\begin{align*} y^{\prime } x -\ln \left (y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.468
19514	17087	\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.469
19515	8397	\begin{align*} y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	4.470
19516	26217	\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}	✓	✓	✓	✓	4.470
19517	5021	\begin{align*} y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \\ \end{align*}	✓	✓	✓	✓	4.471
19518	9651	\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	4.472
19519	3518	\begin{align*} y-\left (x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.473
19520	7537	\begin{align*} x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\ \end{align*}	✓	✓	✓	✓	4.473
19521	6581	\begin{align*} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.474
19522	14447	\begin{align*} \frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.474
19523	7877	\begin{align*} \cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.475
19524	22952	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.476
19525	6929	\begin{align*} x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.477
19526	7939	\begin{align*} x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 y^{\prime } y^{2} x&=0 \\ \end{align*}	✓	✓	✓	✓	4.477
19527	18945	\begin{align*} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.479
19528	26333	\begin{align*} 1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.480
19529	8365	\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.481
19530	23865	\begin{align*} 2 y \ln \left (x \right ) \ln \left (y\right )+x \left (\ln \left (x \right )^{2}+\ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.481
19531	3386	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.482
19532	9060	\begin{align*} \left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	4.482
19533	20218	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.482
19534	5095	\begin{align*} 3 \left (2-y\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.483
19535	8460	\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y&=4 x \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	4.483
19536	24278	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	4.484
19537	26176	\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.484
19538	11621	\begin{align*} \left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y&=0 \\ \end{align*}	✓	✓	✓	✗	4.485
19539	24383	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	4.485
19540	24952	\begin{align*} y^{\prime } t&=y-2 t y \\ \end{align*}	✓	✓	✓	✓	4.485
19541	11839	\begin{align*} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.488
19542	24389	\begin{align*} \left (2 x -1\right ) y+2 \left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.490
19543	10131	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	4.491
19544	17259	\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	4.491
19545	4218	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	4.493
19546	26183	\begin{align*} y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\ \end{align*}	✓	✓	✓	✓	4.493
19547	4784	\begin{align*} y^{\prime } x&=a \,x^{3} \left (-y x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.494
19548	15252	\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right ) \\ 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*} Using Laplace transform method.	✓	✓	✓	✓	4.494
19549	15382	\begin{align*} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.494
19550	16246	\begin{align*} y^{\prime }-3 y^{2} x^{2}&=-3 x^{2} \\ \end{align*}	✓	✓	✓	✓	4.494
19551	23057	\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	4.494
19552	4236	\begin{align*} y \,{\mathrm e}^{2 x} y^{\prime }+2 x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.496
19553	14012	\begin{align*} \left (x +y\right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.496
19554	17238	\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.496
19555	15293	\begin{align*} x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\ y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\ z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.497
19556	16978	\begin{align*} y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.500
19557	22534	\begin{align*} \left (x +y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	4.501
19558	10125	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	4.503
19559	7495	\begin{align*} \cos \left (x +y\right ) y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	4.504
19560	15035	\begin{align*} y^{\prime }-\frac {y}{x +1}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.506
19561	15722	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	4.507
19562	22448	\begin{align*} y^{\prime }+\frac {y}{x}&=1 \\ \end{align*}	✓	✓	✓	✓	4.507
19563	18487	\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.515
19564	25843	\begin{align*} y x -x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.515
19565	5751	\begin{align*} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.516
19566	12353	\begin{align*} 4 y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.516
19567	19305	\begin{align*} 2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.516
19568	24817	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{n} \\ \end{align*}	✓	✓	✓	✗	4.517
19569	17255	\begin{align*} -2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\ \end{align*}	✓	✓	✓	✓	4.518
19570	7678	\begin{align*} x^{2} y^{\prime }+2 y x&=\sinh \left (x \right ) \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.520
19571	8418	\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (-2+y\right )} \\ y \left (0\right ) &= {\frac {3}{2}} \\ \end{align*}	✓	✓	✓	✓	4.520
19572	21431	\begin{align*} 2 y+y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.520
19573	25706	\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.520
19574	10016	\begin{align*} y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.523
19575	11872	\begin{align*} y^{\prime }&=\frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	4.523
19576	17314	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\ \end{align*}	✓	✓	✓	✓	4.523
19577	17907	\begin{align*} \left (x +1\right ) y^{\prime }&=-1+y \\ \end{align*}	✓	✓	✓	✓	4.523
19578	25651	\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align*}	✗	✗	✗	✗	4.523
19579	16364	\begin{align*} x y^{3} y^{\prime }&=y^{4}-x^{2} \\ \end{align*}	✓	✓	✓	✓	4.525
19580	3385	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.526
19581	8691	\begin{align*} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.526
19582	19106	\begin{align*} y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.526
19583	19090	\begin{align*} y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	4.527
19584	4293	\begin{align*} {\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-{\mathrm e}^{y} y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.528
19585	18482	\begin{align*} y^{\prime }&=\frac {\sec \left (x \right )^{2}}{y^{3}+1} \\ \end{align*}	✓	✓	✓	✗	4.529
19586	1535	\begin{align*} y^{\prime }&={| y|}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.531
19587	2842	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.531
19588	18587	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}	✓	✓	✓	✓	4.532
19589	17235	\begin{align*} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✗	✗	✗	4.533
19590	736	\begin{align*} x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✗	4.534
19591	15340	\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.534
19592	3033	\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✗	✓	✗	4.536
19593	3592	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.536
19594	8775	\begin{align*} \left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y&=\left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	4.536
19595	14493	\begin{align*} \cos \left (x \right )^{2}-\cos \left (x \right ) y-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.538
19596	11458	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.541
19597	17165	\begin{align*} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.543
19598	21267	\begin{align*} t x^{\prime \prime }&=x \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	4.543
19599	22054	\begin{align*} y+x^{3}+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.544
19600	4968	\begin{align*} x^{3} y^{\prime }&=3-x^{2}+x^{2} y \\ \end{align*}	✓	✓	✓	✓	4.545