2.3.195 Problems 19401 to 19500

Table 2.921: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19401	1105	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.730
19402	17119	\begin{align*} y^{\prime }&=\frac {3+y}{1+3 x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.731
19403	7554	\begin{align*} x^{3}-y+y^{\prime } x&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.732
19404	7484	\begin{align*} 2 x y^{3}+1+\left (3 y^{2} x^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.733
19405	11414	\begin{align*} y^{\prime } x -x \sqrt {y^{2}+x^{2}}-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.733
19406	12187	\begin{align*} y^{\prime }&=\frac {-2 \cos \left (x \right ) x +2 x^{2} \sin \left (x \right )+2 x +2 y^{2}+4 y \cos \left (x \right ) x -4 y x +\cos \left (2 x \right ) x^{2}+3 x^{2}-4 x^{2} \cos \left (x \right )}{2 x} \\ \end{align*}	✓	✓	✓	✓	2.734
19407	15817	\begin{align*} y^{\prime }&=\left (y+\frac {1}{2}\right ) \left (t +y\right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	2.734
19408	19636	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=f \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.734
19409	4080	\begin{align*} 5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.735
19410	11329	\begin{align*} y^{\prime }+a y \left (y-x \right )-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.735
19411	5026	\begin{align*} y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.737
19412	24378	\begin{align*} y^{2}-3 y-x +\left (2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.738
19413	924	\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}	✓	✓	✓	✓	2.740
19414	1649	\begin{align*} y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.740
19415	4109	\begin{align*} 2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right )&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}	✓	✓	✓	✓	2.740
19416	5251	\begin{align*} x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.740
19417	12329	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.740
19418	18479	\begin{align*} y^{\prime } y&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.740
19419	7246	\begin{align*} 2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.741
19420	4674	\begin{align*} y^{\prime }&=1+a \left (x -y\right ) y \\ \end{align*}	✓	✓	✓	✗	2.743
19421	17067	\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.744
19422	2990	\begin{align*} y^{\prime }-y x&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	2.745
19423	22347	\begin{align*} y^{\prime }&=y \csc \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	2.745
19424	5034	\begin{align*} x \ln \left (x \right ) y^{\prime }&=a x \left (1+\ln \left (x \right )\right )-y \\ \end{align*}	✓	✓	✓	✓	2.747
19425	11394	\begin{align*} y^{\prime } x +a y+b \,x^{n}&=0 \\ \end{align*}	✓	✓	✓	✓	2.747
19426	4307	\begin{align*} y^{\prime }&=\frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	2.748
19427	16143	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (-1+t \right )-3 \delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.749
19428	17798	\begin{align*} x^{\prime \prime }+64 x&=0 \\ x \left (0\right ) &= {\frac {3}{4}} \\ x^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.749
19429	8167	\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	2.750
19430	9934	\begin{align*} y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.750
19431	19848	\begin{align*} e y^{\prime \prime }&=\frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \\ \end{align*}	✓	✓	✓	✓	2.750
19432	19416	\begin{align*} y^{\prime } x +y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.751
19433	4706	\begin{align*} y^{\prime }&=\sqrt {{| y|}} \\ \end{align*}	✓	✓	✓	✓	2.752
19434	10000	\begin{align*} y^{\prime }&=\frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	2.752
19435	4108	\begin{align*} y^{\prime } x +2 y&=\left (3 x +2\right ) {\mathrm e}^{3 x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.753
19436	15924	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.753
19437	17121	\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.753
19438	18486	\begin{align*} y^{\prime }&=\frac {3-2 x}{y} \\ y \left (1\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	2.753
19439	2538	\begin{align*} y^{\prime }&=1-t +y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.754
19440	11599	\begin{align*} \left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.756
19441	16296	\begin{align*} y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.756
19442	4584	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	2.760
19443	7121	\begin{align*} y y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.760
19444	15614	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.760
19445	25784	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.760
19446	6303	\begin{align*} y^{\prime \prime }&=a +b y+2 y^{3} \\ \end{align*}	✓	✓	✓	✗	2.761
19447	4302	\begin{align*} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \\ \end{align*}	✓	✓	✓	✓	2.763
19448	17999	\begin{align*} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	2.763
19449	3673	\begin{align*} y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.764
19450	4246	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.764
19451	25796	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.765
19452	5292	\begin{align*} \left (a^{2} x +y \left (x^{2}-y^{2}\right )\right ) y^{\prime }+x \left (x^{2}-y^{2}\right )&=a^{2} y \\ \end{align*}	✓	✗	✓	✗	2.766
19453	22586	\begin{align*} y^{\prime } \sqrt {x^{3}+1}&=x^{2} y+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.766
19454	17296	\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.767
19455	8727	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	2.768
19456	6886	\begin{align*} y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	2.769
19457	4410	\begin{align*} {\mathrm e}^{x}+3 y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	2.770
19458	5348	\begin{align*} \left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.770
19459	9329	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\ y \left (1\right ) &= {\mathrm e} \\ y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\ \end{align*}	✓	✓	✓	✓	2.770
19460	19198	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\ \end{align*}	✓	✓	✓	✓	2.770
19461	22445	\begin{align*} 2 x +2 x y^{2}+\left (x^{2} y+2 y+3 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.771
19462	7520	\begin{align*} 2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.772
19463	2299	\begin{align*} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.773
19464	19685	\begin{align*} x^{\prime }&=-\lambda x \\ \end{align*}	✓	✓	✓	✓	2.774
19465	15338	\begin{align*} \left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.775
19466	9930	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	2.776
19467	12698	\begin{align*} y^{\prime \prime }&=-\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}} \\ \end{align*}	✗	✓	✓	✗	2.777
19468	15044	\begin{align*} y \left (x -y\right )-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.777
19469	16316	\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.777
19470	17236	\begin{align*} -2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.777
19471	2960	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	2.779
19472	18076	\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	2.779
19473	2490	\begin{align*} y^{\prime }&=1-t +y^{2}-t y^{2} \\ \end{align*}	✓	✓	✓	✓	2.780
19474	8205	\begin{align*} y^{\prime }&=4+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.780
19475	19345	\begin{align*} 2 y-x^{3}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	2.780
19476	21730	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	2.780
19477	18335	\begin{align*} 4 y^{\prime \prime } x +2 y^{\prime }+y&=1 \\ y \left (\infty \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.781
19478	3465	\begin{align*} y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\ \end{align*}	✓	✓	✓	✓	2.782
19479	21988	\begin{align*} y^{\prime }&=\frac {x^{2}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.782
19480	1245	\begin{align*} 3 t +2 y&=-t y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.783
19481	11678	\begin{align*} {y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	2.783
19482	16257	\begin{align*} y^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	2.783
19483	19471	\begin{align*} y^{\prime \prime }&=4 y \\ \end{align*}	✓	✓	✓	✓	2.785
19484	24893	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.785
19485	9016	\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.786
19486	9192	\begin{align*} y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	2.786
19487	12041	\begin{align*} y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \\ \end{align*}	✗	✓	✓	✗	2.786
19488	14445	\begin{align*} \frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.786
19489	16240	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.786
19490	21717	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.787
19491	20919	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.788
19492	22533	\begin{align*} 2 x^{2}-{\mathrm e}^{x} y-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.788
19493	22957	\begin{align*} \left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.788
19494	23881	\begin{align*} 3 y^{2} x^{2}-4 y+\left (3 y^{2}-4 x +2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.788
19495	3602	\begin{align*} \left (x -a \right ) \left (-b +x \right ) y^{\prime }-y+c&=0 \\ \end{align*}	✓	✓	✓	✓	2.789
19496	7126	\begin{align*} y^{\prime \prime }&=\frac {3 k y^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	2.789
19497	15622	\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \\ y \left (-1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.789
19498	703	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	2.790
19499	8777	\begin{align*} y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.790
19500	24907	\begin{align*} 4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	2.790