2.3.207 Problems 20601 to 20700

Table 2.945: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20601	3670	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=y^{3} \sin \left (x \right )^{3} \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.581
20602	20524	\begin{align*} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=2 x \\ \end{align*}	✓	✓	✓	✗	3.581
20603	5596	\begin{align*} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.582
20604	11651	\begin{align*} \cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.582
20605	18550	\begin{align*} y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	3.582
20606	10021	\begin{align*} f^{\prime } x -f&=\frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \\ \end{align*}	✓	✓	✓	✗	3.583
20607	15350	\begin{align*} x +y+\left (y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.583
20608	24975	\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	3.584
20609	1579	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.586
20610	4938	\begin{align*} x \left (1-x \right ) y^{\prime }&=a +2 \left (-x +2\right ) y \\ \end{align*}	✓	✓	✓	✓	3.586
20611	708	\begin{align*} y^{\prime } x +2 y&=3 x \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.587
20612	19458	\begin{align*} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.587
20613	17343	\begin{align*} y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	3.588
20614	11616	\begin{align*} \left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 y^{4} x +x&=0 \\ \end{align*}	✓	✓	✓	✓	3.590
20615	21847	\begin{align*} R q^{\prime }+\frac {q}{c}&=E \\ q \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.590
20616	4351	\begin{align*} y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.591
20617	7872	\begin{align*} 1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.591
20618	11410	\begin{align*} y^{\prime } x +f \left (x \right ) \left (y^{2}-x^{2}\right )-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.594
20619	20262	\begin{align*} y^{\prime }&=\frac {1+2 x -y}{x +2 y-3} \\ \end{align*}	✓	✓	✓	✓	3.595
20620	11406	\begin{align*} y^{\prime } x +x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b}&=0 \\ \end{align*}	✓	✓	✓	✗	3.596
20621	19316	\begin{align*} y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.596
20622	22015	\begin{align*} y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\ \end{align*}	✓	✓	✓	✓	3.600
20623	20797	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{3} \sin \left (x^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	3.601
20624	6981	\begin{align*} x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.602
20625	11440	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\ \end{align*}	✓	✓	✓	✓	3.604
20626	6486	\begin{align*} 3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.605
20627	9056	\begin{align*} y^{\prime }&=\frac {x y}{y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.605
20628	4796	\begin{align*} y^{\prime } x&=y \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.606
20629	18568	\begin{align*} 3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.611
20630	7869	\begin{align*} x y^{\prime } y&=\left (1+y\right ) \left (1-x \right ) \\ \end{align*}	✓	✓	✓	✓	3.612
20631	9972	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.612
20632	11477	\begin{align*} 2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3&=0 \\ \end{align*}	✓	✓	✓	✓	3.615
20633	13837	\begin{align*} \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (k x +d \right ) y^{\prime }-k y&=0 \\ \end{align*}	✓	✓	✓	✗	3.618
20634	17991	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } y&=y^{2} \left ({\mathrm e}^{2 x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	3.618
20635	20694	\begin{align*} y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x y^{2}+x \right ) y^{\prime }}{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.618
20636	11307	\begin{align*} y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✓	3.619
20637	24332	\begin{align*} k \,{\mathrm e}^{2 v}-u -2 \,{\mathrm e}^{2 v} \left ({\mathrm e}^{2 v}+k u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.619
20638	6898	\begin{align*} y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.622
20639	4634	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\ \end{align*}	✓	✓	✓	✗	3.623
20640	17327	\begin{align*} \tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.624
20641	1803	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7&=0 \\ \end{align*}	✓	✓	✓	✓	3.625
20642	21259	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.625
20643	5040	\begin{align*} y^{\prime } y+f \left (x \right )&=g \left (x \right ) y \\ \end{align*}	✗	✗	✗	✗	3.628
20644	7746	\begin{align*} \left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \\ \end{align*}	✓	✓	✓	✓	3.631
20645	9630	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.631
20646	21481	\begin{align*} y^{\prime \prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.631
20647	12077	\begin{align*} y^{\prime }&=\frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}} \\ \end{align*}	✓	✓	✓	✗	3.634
20648	15802	\begin{align*} y^{\prime }&=t y^{2}+2 y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.634
20649	16220	\begin{align*} x y^{\prime } y&=y^{2}+9 \\ \end{align*}	✓	✓	✓	✓	3.635
20650	5070	\begin{align*} \left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.636
20651	25004	\begin{align*} y^{\prime }&=\frac {4 t -3 y}{t -y} \\ \end{align*}	✓	✓	✓	✗	3.636
20652	4797	\begin{align*} y^{\prime } x +y \left (1-x y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.637
20653	15605	\begin{align*} x y \left (1-y\right )-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.638
20654	25013	\begin{align*} t y+y^{\prime }&=t y^{3} \\ \end{align*}	✓	✓	✓	✓	3.640
20655	6826	\begin{align*} x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.641
20656	17947	\begin{align*} x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right )&=-1 \\ y \left (\infty \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.641
20657	17047	\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	3.643
20658	11310	\begin{align*} y^{\prime }+\tan \left (x \right ) y-\sin \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.645
20659	17878	\begin{align*} \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.645
20660	23119	\begin{align*} y^{\prime }&=-\frac {y^{2}+x^{2}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	3.645
20661	11408	\begin{align*} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.647
20662	13942	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y&=0 \\ \end{align*}	✗	✓	✓	✗	3.647
20663	15957	\begin{align*} y^{\prime }&=t^{2} y^{3}+y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.648
20664	25695	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.648
20665	4617	\begin{align*} y^{\prime }&=x^{2} \left (a \,x^{3}+b y\right ) \\ \end{align*}	✓	✓	✓	✓	3.649
20666	6663	\begin{align*} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	3.649
20667	11479	\begin{align*} \left (a \,x^{2}+b x +c \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.649
20668	9007	\begin{align*} y^{\prime } y&=x \\ \end{align*}	✓	✓	✓	✓	3.650
20669	11555	\begin{align*} 2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.650
20670	19776	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	3.653
20671	8377	\begin{align*} y^{\prime }&=y^{2}-4 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	3.654
20672	19859	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.654
20673	1626	\begin{align*} y^{\prime }&=\frac {y+{\mathrm e}^{-\frac {y}{x}} x}{x} \\ \end{align*}	✓	✓	✓	✓	3.656
20674	20434	\begin{align*} y-y^{\prime } x&=y^{\prime } y+x \\ \end{align*}	✓	✓	✓	✓	3.656
20675	11873	\begin{align*} y^{\prime }&=\frac {x}{-y+F \left (y^{2}+x^{2}\right )} \\ \end{align*}	✓	✓	✓	✗	3.657
20676	25824	\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.658
20677	11343	\begin{align*} a y^{3} x +b y^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.662
20678	15528	\begin{align*} y^{\prime }&=y^{2}-4 \\ \end{align*}	✓	✓	✓	✓	3.664
20679	22426	\begin{align*} y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.664
20680	22972	\begin{align*} y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	3.664
20681	22429	\begin{align*} \frac {y}{\left (x +y\right )^{2}}-1+\left (1-\frac {x}{\left (x +y\right )^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.665
20682	10120	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	3.668
20683	15158	\begin{align*} x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.668
20684	17202	\begin{align*} t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.668
20685	59	\begin{align*} y^{\prime }&={\mathrm e}^{x} y \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	3.670
20686	4830	\begin{align*} y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.670
20687	3555	\begin{align*} y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x +y \\ \end{align*}	✓	✓	✓	✓	3.671
20688	5037	\begin{align*} y^{\prime } y+x^{3}+y&=0 \\ \end{align*}	✗	✗	✗	✗	3.671
20689	12450	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.671
20690	4686	\begin{align*} y^{\prime }&=y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.672
20691	804	\begin{align*} y^{\prime }&=\frac {x +3 y}{-3 x +y} \\ \end{align*}	✓	✓	✓	✓	3.673
20692	11344	\begin{align*} y^{\prime }-x \left (2+x \right ) y^{3}-\left (x +3\right ) y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.673
20693	13989	\begin{align*} y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	3.673
20694	23064	\begin{align*} r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.673
20695	11786	\begin{align*} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.674
20696	14008	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.674
20697	15348	\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.675
20698	6589	\begin{align*} 4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.678
20699	15156	\begin{align*} y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y&=\tan \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	3.678
20700	23915	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	3.678