2.3.167 Problems 16601 to 16700

Table 2.877: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16601	26079	\begin{align*} 2 y y^{\prime } x +1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.574
16602	2691	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.576
16603	9013	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.576
16604	20678	\begin{align*} \cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.576
16605	3459	\begin{align*} y \left (2 y^{2} x^{2}+1\right ) y^{\prime }+x \left (1+y^{4}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.577
16606	8466	\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=10 \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.577
16607	12176	\begin{align*} y^{\prime }&=\frac {x +1+y^{4}-2 y^{2} x^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 y^{2} x^{4}-x^{6}}{y} \\ \end{align*}	✓	✓	✓	✗	2.577
16608	15909	\begin{align*} -2 y+y^{\prime }&=7 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.577
16609	12554	\begin{align*} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.578
16610	1545	\begin{align*} y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.579
16611	15387	\begin{align*} x +y y^{\prime }&=\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.579
16612	18546	\begin{align*} y+\left (t -4\right ) t y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.579
16613	21070	\begin{align*} y-x^{{1}/{3}}+\left (x +y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.579
16614	2808	\begin{align*} x^{\prime }&=x \left (1-x\right ) \\ \end{align*}	✓	✓	✓	✓	2.581
16615	13839	\begin{align*} \left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+3 \left (a x +b \right ) y^{\prime }+d y&=0 \\ \end{align*}	✓	✓	✓	✗	2.581
16616	15952	\begin{align*} y^{\prime }&=2 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.581
16617	5430	\begin{align*} {y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+y^{4} x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.582
16618	16555	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.582
16619	24126	\begin{align*} v^{\prime }&=-\frac {v}{p} \\ \end{align*}	✓	✓	✓	✓	2.582
16620	8868	\begin{align*} y^{\prime }-2 y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	2.583
16621	9088	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.583
16622	26158	\begin{align*} x&=y^{\prime }+\arcsin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.583
16623	13003	\begin{align*} 3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.584
16624	16477	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	2.584
16625	17036	\begin{align*} y^{\prime }&=y+\frac {1}{1-t} \\ \end{align*}	✓	✓	✓	✓	2.585
16626	20286	\begin{align*} x +y y^{\prime }&=\frac {a^{2} \left (-y+y^{\prime } x \right )}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	2.585
16627	766	\begin{align*} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.586
16628	1100	\begin{align*} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.586
16629	11841	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.586
16630	1169	\begin{align*} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (-3\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.587
16631	10273	\begin{align*} c y^{\prime }&=a x +y \\ \end{align*}	✓	✓	✓	✓	2.587
16632	19138	\begin{align*} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.587
16633	26200	\begin{align*} y^{\prime }&=y+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.588
16634	603	\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}	✓	✓	✓	✓	2.589
16635	5634	\begin{align*} {y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.589
16636	12879	\begin{align*} y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	2.589
16637	13235	\begin{align*} y^{\prime }&=-a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \\ \end{align*}	✓	✓	✓	✗	2.589
16638	19987	\begin{align*} x^{2} \left (-y^{\prime } x +y\right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.589
16639	13250	\begin{align*} 2 x^{2} y^{\prime }&=2 y^{2}+y x -2 a^{2} x \\ \end{align*}	✓	✓	✓	✗	2.590
16640	13877	\begin{align*} x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y&=c \,x^{2} \left (x -a \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.591
16641	25452	\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	2.591
16642	797	\begin{align*} 3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.592
16643	8302	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.593
16644	6346	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.594
16645	13223	\begin{align*} a \,x^{2} \left (x -1\right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s&=0 \\ \end{align*}	✓	✓	✗	✗	2.594
16646	25895	\begin{align*} y^{\prime } x +y&=y y^{\prime } x -y x \\ \end{align*}	✓	✓	✓	✓	2.594
16647	2586	\begin{align*} 3 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (t \right ) {\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.595
16648	18594	\begin{align*} y y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	2.595
16649	25754	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.595
16650	17171	\begin{align*} x^{\prime }&=x+t +1 \\ x \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.596
16651	18541	\begin{align*} y^{\prime }-6 y&=t^{6} {\mathrm e}^{6 t} \\ \end{align*}	✓	✓	✓	✓	2.596
16652	1712	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.598
16653	13900	\begin{align*} x^{6} y^{\prime \prime }+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✗	2.598
16654	22488	\begin{align*} y y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	2.599
16655	14174	\begin{align*} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✗	✓	2.600
16656	19902	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.600
16657	4651	\begin{align*} y^{\prime }&=f \left (x \right )+g \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.601
16658	15815	\begin{align*} y^{\prime }&=3 y \left (1-y\right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	2.601
16659	3294	\begin{align*} y&=y^{\prime } x \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.602
16660	7042	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.602
16661	16439	\begin{align*} y^{\prime } x +3 y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	2.602
16662	17079	\begin{align*} y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	2.602
16663	25476	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.603
16664	4752	\begin{align*} y^{\prime } x +x^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.606
16665	10427	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.606
16666	17321	\begin{align*} y-x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.606
16667	14389	\begin{align*} x^{\prime }&=3 y-3 x \\ y^{\prime }&=x+2 y-1 \\ \end{align*}	✓	✓	✓	✓	2.607
16668	19995	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.607
16669	12441	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.608
16670	25901	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.608
16671	3532	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\ \end{align*}	✓	✓	✓	✓	2.609
16672	12919	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-a&=0 \\ \end{align*}	✓	✓	✓	✗	2.609
16673	15928	\begin{align*} y^{\prime }&=t^{2} y+4 \\ \end{align*}	✓	✓	✓	✓	2.609
16674	3669	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.611
16675	19790	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.611
16676	4075	\begin{align*} y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.612
16677	15124	\begin{align*} x \left (1+y\right )^{2}&=\left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.612
16678	24136	\begin{align*} y^{\prime } x +y+x y \left (1+y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.613
16679	14659	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.615
16680	15613	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	2.615
16681	16139	\begin{align*} y^{\prime \prime }+3 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.615
16682	15584	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.616
16683	18511	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\ \end{align*}	✓	✓	✓	✓	2.616
16684	24375	\begin{align*} 3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.616
16685	14057	\begin{align*} a^{2} y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.618
16686	17353	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.618
16687	9127	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.619
16688	14371	\begin{align*} x^{\prime \prime }+x&=3 \delta \left (t -2 \pi \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.619
16689	19015	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\ x_{2}^{\prime }&=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\ x_{3}^{\prime }&=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\ x_{4}^{\prime }&=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \\ \end{align*}	✓	✓	✓	✓	2.619
16690	8503	\begin{align*} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.620
16691	14181	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.623
16692	15341	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.623
16693	17802	\begin{align*} x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= -2 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.623
16694	4756	\begin{align*} y^{\prime } x&=x \sin \left (x \right )-y \\ \end{align*}	✓	✓	✓	✓	2.624
16695	12922	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.624
16696	4251	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.625
16697	15816	\begin{align*} y^{\prime }&=2 y-t \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.625
16698	19341	\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\ \end{align*}	✓	✓	✓	✓	2.625
16699	7310	\begin{align*} y y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	2.626
16700	13002	\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.626