2.3.215 Problems 21401 to 21500

Table 2.1003: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
21401	21844	\begin{align*} 4 x^{2} y^{2} y^{\prime }-3 x y^{3}&=x^{2} y^{3}+2 x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.694
21402	9191	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	5.695
21403	12120	\begin{align*} y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+x \,{\mathrm e}^{-\frac {y}{x}}+x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\ \end{align*}	✓	✓	✓	✓	5.697
21404	19417	\begin{align*} -y^{2}+x^{2} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	5.697
21405	15051	\begin{align*} y&=x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\ \end{align*}	✓	✓	✗	✓	5.699
21406	1688	\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.700
21407	1351	\begin{align*} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=4 t^{2} \\ \end{align*}	✓	✓	✓	✓	5.702
21408	27408	\begin{align*} 2 x y^{\prime }+y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	5.702
21409	8160	\begin{align*} y^{2}-1+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.703
21410	26312	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=-\frac {\sin \left (x \right )^{2}}{x^{2}} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.704
21411	11470	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.707
21412	15370	\begin{align*} y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	5.707
21413	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*}	✓	✓	✓	✓	5.708
21414	6247	\begin{align*} a^{2} y+2 x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.709
21415	2959	\begin{align*} y^{\prime }+2 y x&=2 x \,{\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.711
21416	112	\begin{align*} x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✗	5.714
21417	25836	\begin{align*} y^{\prime }&=-\frac {y}{x -3} \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.717
21418	6321	\begin{align*} y^{\prime \prime }&=\operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	5.718
21419	24906	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	5.719
21420	9390	\begin{align*} x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.720
21421	9043	\begin{align*} y^{\prime \prime }+\sin \left (y\right )&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	5.722
21422	3635	\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.723
21423	1726	\begin{align*} a y+b x y+\left (c x +d x y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.724
21424	19400	\begin{align*} 3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.724
21425	22226	\begin{align*} x y^{\prime \prime }-3 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.724
21426	24350	\begin{align*} \left (2 x -y+3\right ) y^{\prime }+2&=0 \\ \end{align*}	✓	✓	✓	✓	5.724
21427	13958	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b \,{\mathrm e}^{\mu x}-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+c \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{2 \mu x} b^{2}+b \left (\mu -\lambda \right ) {\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	5.727
21428	24292	\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.727
21429	3673	\begin{align*} y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.730
21430	13782	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.730
21431	18585	\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.730
21432	6487	\begin{align*} 3 y y^{\prime \prime }&=5 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.731
21433	21261	\begin{align*} x^{\prime \prime }+x+8 x^{7}&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= a \\ \end{align*}	✓	✓	✗	✗	5.731
21434	12238	\begin{align*} y^{\prime }&=\frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1} \\ \end{align*}	✓	✓	✓	✗	5.732
21435	4885	\begin{align*} x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.733
21436	7012	\begin{align*} x y^{\prime }&=x +y+{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}	✓	✓	✓	✗	5.734
21437	903	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	5.736
21438	2932	\begin{align*} y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.736
21439	6528	\begin{align*} \sqrt {a^{2}+x^{2}}\, \left (b {y^{\prime }}^{2}+y y^{\prime \prime }\right )&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	5.736
21440	4926	\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \\ \end{align*}	✓	✓	✓	✓	5.738
21441	4349	\begin{align*} y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.740
21442	6160	\begin{align*} 5 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.741
21443	11464	\begin{align*} x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.742
21444	5652	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.744
21445	16316	\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.744
21446	9004	\begin{align*} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.746
21447	1691	\begin{align*} y \sin \left (y x \right )+x y^{2} \cos \left (y x \right )+\left (x \sin \left (y x \right )+x y^{2} \cos \left (y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.747
21448	1660	\begin{align*} y^{\prime }&=\frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.748
21449	21031	\begin{align*} x^{\prime }+\frac {\sin \left (t \right ) x}{1+{\mathrm e}^{t}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.748
21450	11985	\begin{align*} y^{\prime }&=\frac {-y \,{\mathrm e}^{x}+y x -x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (x -{\mathrm e}^{x}\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.749
21451	4874	\begin{align*} x^{2} y^{\prime }&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	5.750
21452	14721	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=-6 x^{3}+4 x^{2} \\ y \left (2\right ) &= 4 \\ y^{\prime }\left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.752
21453	24338	\begin{align*} x y^{\prime }-y&=y \\ \end{align*}	✓	✓	✓	✓	5.753
21454	4677	\begin{align*} y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\ \end{align*}	✓	✓	✓	✓	5.754
21455	4679	\begin{align*} y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	5.757
21456	11427	\begin{align*} x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right )&=0 \\ \end{align*}	✗	✓	✓	✗	5.757
21457	2516	\begin{align*} 2 t -2 \,{\mathrm e}^{y t} \sin \left (2 t \right )+{\mathrm e}^{y t} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{y t} t \cos \left (2 t \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.759
21458	12260	\begin{align*} y^{\prime }&=\frac {x^{3} y^{3}+6 x^{2} y^{2}+12 y x +8+2 x}{x^{3}} \\ \end{align*}	✓	✓	✓	✓	5.762
21459	13019	\begin{align*} \left (y^{2}-1\right ) \left (y^{2} a^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-y^{2} a^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 y^{2} a^{2}\right ) y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✗	✓	✗	5.762
21460	6292	\begin{align*} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.763
21461	9194	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	5.766
21462	9989	\begin{align*} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \\ \end{align*}	✓	✓	✓	✓	5.766
21463	18512	\begin{align*} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	5.766
21464	26311	\begin{align*} 2 x^{2} y^{\prime }-y x&=2 x \cos \left (x \right )-2 \sin \left (x \right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	5.767
21465	27256	\begin{align*} 2 y^{\prime }+x&=4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✗	5.768
21466	4667	\begin{align*} y^{\prime }&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	5.769
21467	14538	\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.770
21468	4868	\begin{align*} x^{2} y^{\prime }&=a +b x y \\ \end{align*}	✓	✓	✓	✓	5.773
21469	9136	\begin{align*} 2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.773
21470	24843	\begin{align*} y {y^{\prime }}^{3}-3 x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.774
21471	2981	\begin{align*} 3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.775
21472	17060	\begin{align*} y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\ y \left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.776
21473	25474	\begin{align*} y^{\prime }&=a y-b y^{n} \\ \end{align*}	✓	✓	✓	✗	5.776
21474	12096	\begin{align*} y^{\prime }&=\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \\ \end{align*}	✓	✓	✓	✓	5.777
21475	3774	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+9 y&=9 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.778
21476	14543	\begin{align*} 2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.778
21477	5521	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\ \end{align*}	✓	✓	✓	✓	5.782
21478	25055	\begin{align*} t y^{\prime }&=2 y-t \\ \end{align*}	✓	✓	✓	✓	5.784
21479	19368	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.785
21480	12259	\begin{align*} y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \\ \end{align*}	✓	✓	✓	✓	5.787
21481	19745	\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	5.787
21482	5322	\begin{align*} \left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime }&=\left (2+y^{3}\right ) y \\ \end{align*}	✓	✓	✓	✓	5.788
21483	18562	\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✗	✓	✓	5.789
21484	8304	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	5.790
21485	17866	\begin{align*} y^{\prime }&=-\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.790
21486	21438	\begin{align*} y^{\prime }+\frac {y}{x}&=3 x \\ \end{align*}	✓	✓	✓	✓	5.792
21487	8429	\begin{align*} x y^{\prime }+2 y&=3 \\ \end{align*}	✓	✓	✓	✓	5.794
21488	13234	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1} \\ \end{align*}	✓	✗	✓	✗	5.794
21489	17237	\begin{align*} -4 x^{3}+6 y \sin \left (6 y x \right )+\left (4 y^{3}+6 x \sin \left (6 y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.794
21490	5374	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.795
21491	6967	\begin{align*} r^{\prime }&=\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	5.796
21492	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.	✓	✓	✓	✓	5.796
21493	22634	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	5.796
21494	25772	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	5.797
21495	3600	\begin{align*} y^{\prime }&=\frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )} \\ \end{align*}	✓	✓	✓	✓	5.800
21496	15240	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.800
21497	21254	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ \end{align*}	✓	✓	✓	✗	5.801
21498	26149	\begin{align*} x y^{\prime }&=y \tan \left (\ln \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.801
21499	17159	\begin{align*} y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.802
21500	26891	\begin{align*} 4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.802