2.3.157 Problems 15601 to 15700

Table 2.845: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15601	4110	\begin{align*} y y^{\prime } x&=\left (x +1\right ) \left (1+y\right ) \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.513
15602	1569	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.514
15603	3047	\begin{align*} x^{\prime }&=x+x^{2} {\mathrm e}^{\theta } \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.516
15604	6825	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.516
15605	13711	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	3.516
15606	9124	\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.517
15607	23247	\begin{align*} x^{2} y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }-2&=0 \\ \end{align*}	✓	✓	✓	✓	3.517
15608	23886	\begin{align*} 3 x^{2} {\mathrm e}^{x^{3}}+{\mathrm e}^{2 y}+\left (2 x \,{\mathrm e}^{2 y}-3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.517
15609	13796	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.518
15610	16287	\begin{align*} \cos \left (-4 y+8 x -3\right ) y^{\prime }&=2+2 \cos \left (-4 y+8 x -3\right ) \\ \end{align*}	✓	✓	✓	✓	3.518
15611	20198	\begin{align*} -y+y^{\prime } x +y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.518
15612	20805	\begin{align*} y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y&=\sin \left (x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	3.518
15613	1700	\begin{align*} \left (2 x -1\right ) \left (-1+y\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.519
15614	13972	\begin{align*} \left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.519
15615	23250	\begin{align*} 2 y-3 y^{\prime \prime } x +4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.520
15616	5066	\begin{align*} \left (2 x -y+3\right ) y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	3.522
15617	5834	\begin{align*} -2 a \left (-2 a \,x^{2}+1\right ) y-4 a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.522
15618	4736	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\ \end{align*}	✓	✓	✓	✓	3.524
15619	23884	\begin{align*} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.524
15620	1567	\begin{align*} y^{\prime } x +2 y&=8 x^{2} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.525
15621	12323	\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (3 x^{2}+2 n -1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.525
15622	22547	\begin{align*} 2 y+3 x +y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.525
15623	12021	\begin{align*} y^{\prime }&=\frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	3.526
15624	12289	\begin{align*} y^{\prime \prime }+l y&=0 \\ \end{align*}	✓	✓	✓	✓	3.527
15625	25278	\begin{align*} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \\ \end{align*}	✓	✓	✓	✗	3.527
15626	1568	\begin{align*} y^{\prime } x -2 y&=-x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.528
15627	5254	\begin{align*} x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.528
15628	218	\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*}	✓	✓	✓	✓	3.529
15629	5942	\begin{align*} \left (b x +a \right ) y+y^{\prime }+2 y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	3.530
15630	16628	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=20 \\ \end{align*}	✓	✓	✓	✓	3.531
15631	1496	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	3.533
15632	18473	\begin{align*} y^{\prime }&=\frac {x^{4}}{y} \\ \end{align*}	✓	✓	✓	✓	3.533
15633	23672	\begin{align*} x^{2} y^{\prime \prime }-\left (2+x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.533
15634	9583	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.535
15635	17983	\begin{align*} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.535
15636	13261	\begin{align*} \left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 y x +\left (1-a \right ) x^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✗	3.536
15637	21065	\begin{align*} 2 x^{2}+1&=\left (y^{5}-1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.537
15638	4333	\begin{align*} x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.538
15639	2977	\begin{align*} y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.539
15640	22464	\begin{align*} y+x^{3}+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.539
15641	25593	\begin{align*} y^{\prime \prime }+y^{\prime }&=1+t \\ \end{align*}	✓	✓	✓	✓	3.539
15642	5313	\begin{align*} x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.540
15643	20636	\begin{align*} y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 y \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.540
15644	21970	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.543
15645	25517	\begin{align*} y^{\prime \prime }&=-9 y \\ \end{align*}	✓	✓	✓	✓	3.543
15646	13631	\begin{align*} x \left (2 a x y+b \right ) y^{\prime }&=-a \left (m +3\right ) x y^{2}-b \left (m +2\right ) y+c \,x^{m} \\ \end{align*}	✓	✓	✓	✗	3.544
15647	8664	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.545
15648	17157	\begin{align*} y^{\prime }&=\frac {1}{x +y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.545
15649	1174	\begin{align*} y^{\prime }&=-\frac {4 t}{y} \\ \end{align*}	✓	✓	✓	✓	3.546
15650	13710	\begin{align*} y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+x^{n -1} a n +c \,x^{m -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.546
15651	23186	\begin{align*} y+\cos \left (x \right )+\left (x +\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.546
15652	24121	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.546
15653	4673	\begin{align*} y^{\prime }&=f \left (x \right )+a y+b y^{2} \\ \end{align*}	✗	✗	✗	✗	3.547
15654	775	\begin{align*} 3 y+x^{4} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.549
15655	11726	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.549
15656	7010	\begin{align*} y^{\prime } x -y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.550
15657	14852	\begin{align*} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.550
15658	12644	\begin{align*} y^{\prime \prime }&=-\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \\ \end{align*}	✓	✓	✓	✗	3.552
15659	20891	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	3.552
15660	21046	\begin{align*} x^{\prime }&=t x-t^{3} \\ x \left (a \right ) &= a^{2} \\ \end{align*}	✓	✓	✓	✓	3.553
15661	25107	\begin{align*} y^{\prime \prime }-4 y^{\prime }-21 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.553
15662	6559	\begin{align*} \left (-\left (1-y\right ) \left (-y+a \right )+y \left (1-y\right )+\left (-y+a \right ) y\right ) {y^{\prime }}^{2}+2 \left (1-y\right ) \left (-y+a \right ) y y^{\prime \prime }&=\operatorname {a3} \left (1-y\right )^{2} \left (-y+a \right )^{2}+\operatorname {a1} \left (1-y\right )^{2} y^{2}+\operatorname {a2} \left (-y+a \right )^{2} y^{2}+\operatorname {a0} \left (-y+a \right )^{2} y^{2} \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	3.556
15663	14914	\begin{align*} y x +y^{2}+x^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.556
15664	1182	\begin{align*} y^{\prime }&=a y+b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.557
15665	6841	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.557
15666	23371	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.557
15667	5548	\begin{align*} y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y&=0 \\ \end{align*}	✓	✓	✓	✗	3.558
15668	5829	\begin{align*} y a^{2} x^{2}-2 a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.558
15669	11324	\begin{align*} y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.558
15670	13701	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (a \,x^{3} b +a c \,x^{2}+b \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.558
15671	24215	\begin{align*} x^{3}+x y^{2}+y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.559
15672	17818	\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.560
15673	23333	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.560
15674	4362	\begin{align*} \left (y^{3}+\frac {x}{y}\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.561
15675	5130	\begin{align*} y y^{\prime } x&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	3.561
15676	17210	\begin{align*} 2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.561
15677	9194	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.562
15678	17173	\begin{align*} y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.562
15679	13720	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (x^{n +m} a b +b \left (m +1\right ) x^{m -1}-a \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	3.563
15680	22347	\begin{align*} y^{\prime }&=y \csc \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	3.563
15681	22470	\begin{align*} y-x \sqrt {x^{2}+y^{2}}+\left (x -y \sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.563
15682	12371	\begin{align*} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	3.564
15683	20270	\begin{align*} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.565
15684	18494	\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\ y \left (0\right ) &= -2^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.566
15685	21765	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.566
15686	23129	\begin{align*} y^{\prime }-y x&=-x^{2}+1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.566
15687	23313	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.567
15688	25205	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.567
15689	9887	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.571
15690	12242	\begin{align*} y^{\prime }&=\frac {4 x \left (-1+a \right ) \left (1+a \right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 y a^{2} x^{2}-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 y^{2} x^{4}+x^{6}} \\ \end{align*}	✓	✓	✓	✗	3.571
15691	21164	\begin{align*} x^{\prime \prime }-2 x^{\prime } \left (x-1\right )&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.571
15692	10005	\begin{align*} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\ \end{align*}	✗	✗	✗	✗	3.572
15693	22719	\begin{align*} q^{\prime \prime }+q&=t \sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.572
15694	24120	\begin{align*} \left (1-x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.573
15695	13379	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	3.574
15696	19256	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.574
15697	7133	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.575
15698	25015	\begin{align*} \left (-t^{2}+1\right ) y^{\prime }-t y&=5 t y^{2} \\ \end{align*}	✓	✓	✓	✓	3.575
15699	11773	\begin{align*} y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.576
15700	13995	\begin{align*} 4 y^{\prime } x +3 y+{\mathrm e}^{x} x^{4} y^{5}&=0 \\ \end{align*}	✓	✓	✓	✓	3.576