2.3.205 Problems 20401 to 20500

Table 2.953: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20401	5473	\begin{align*} x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.756
20402	26149	\begin{align*} y^{\prime } x&=y \tan \left (\ln \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.756
20403	19292	\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	5.757
20404	22514	\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}	✓	✓	✓	✓	5.760
20405	20226	\begin{align*} x \cos \left (y\right )^{2}&=y \cos \left (x \right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	5.763
20406	22611	\begin{align*} y^{\prime }+y^{2}&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✗	5.767
20407	7702	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\ \end{align*}	✓	✓	✓	✓	5.770
20408	23399	\begin{align*} 3 y^{\prime \prime } x -4 y^{\prime }+\frac {5 y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	5.770
20409	11978	\begin{align*} y^{\prime }&=\frac {y \ln \left (x -1\right )+x^{4}+x^{3}+y^{2} x^{2}+x y^{2}}{\ln \left (x -1\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.771
20410	14906	\begin{align*} T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.773
20411	9016	\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.774
20412	16201	\begin{align*} y^{\prime }-y^{2}&=x \\ \end{align*}	✓	✓	✓	✗	5.774
20413	14072	\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.776
20414	11857	\begin{align*} a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	5.777
20415	23370	\begin{align*} 3 x^{2} y^{\prime \prime }+4 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	5.778
20416	13729	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{n} \left (-b \,x^{n +1}+a +n \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.779
20417	23014	\begin{align*} y^{\prime \prime }-8 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.780
20418	16304	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\ \end{align*}	✓	✓	✓	✓	5.785
20419	11783	\begin{align*} \left (-x +y\right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (1+y^{\prime }\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.787
20420	22287	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✗	✗	✗	5.787
20421	26217	\begin{align*} y^{\prime }&=a^{x +y} \\ \end{align*}	✓	✓	✓	✓	5.793
20422	15941	\begin{align*} y^{\prime }&=\frac {\left (t^{2}-4\right ) \left (1+y\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )} \\ \end{align*}	✓	✓	✓	✓	5.795
20423	11471	\begin{align*} x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\ \end{align*}	✓	✓	✓	✓	5.796
20424	12181	\begin{align*} y^{\prime }&=\frac {\left (y-a \ln \left (y\right ) x +x^{2}\right ) y}{\left (-y \ln \left (y\right )-y \ln \left (x \right )-y+a x \right ) x} \\ \end{align*}	✓	✓	✓	✗	5.796
20425	25772	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	5.797
20426	18058	\begin{align*} x^{2}+y^{2}-y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.799
20427	5636	\begin{align*} {y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.802
20428	5652	\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.805
20429	6010	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	5.805
20430	12020	\begin{align*} y^{\prime }&=\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \\ \end{align*}	✓	✓	✓	✗	5.808
20431	12701	\begin{align*} y^{\prime \prime }&=-\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	5.808
20432	2981	\begin{align*} 3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.809
20433	7530	\begin{align*} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.809
20434	16357	\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\ \end{align*}	✓	✓	✓	✓	5.809
20435	4667	\begin{align*} y^{\prime }&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	5.810
20436	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*}	✓	✗	✓	✗	5.813
20437	14197	\begin{align*} x^{\prime }+2 x&=t^{2}+4 t +7 \\ \end{align*}	✓	✓	✓	✓	5.813
20438	12214	\begin{align*} y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-y x -\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 y^{2} x^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \\ \end{align*}	✓	✓	✓	✗	5.815
20439	1140	\begin{align*} r^{\prime }&=\frac {r^{2}}{x} \\ r \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.816
20440	11979	\begin{align*} y^{\prime }&=\frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.817
20441	2986	\begin{align*} y^{\prime }-y x&=\sqrt {y}\, x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.822
20442	4885	\begin{align*} x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.822
20443	5604	\begin{align*} 3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	5.823
20444	4426	\begin{align*} y+\left (y x -x -y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.826
20445	13246	\begin{align*} y^{\prime } x&=x^{2 n} a y^{2}+\left (b \,x^{n}-n \right ) y+c \\ \end{align*}	✓	✓	✓	✗	5.826
20446	15545	\begin{align*} y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\ \end{align*}	✗	✗	✗	✗	5.828
20447	17202	\begin{align*} t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.829
20448	13727	\begin{align*} y^{\prime \prime } x +\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\ \end{align*}	✗	✓	✓	✗	5.832
20449	1800	\begin{align*} \left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-3-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.833
20450	15547	\begin{align*} y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.839
20451	7021	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.840
20452	1726	\begin{align*} a y+b x y+\left (c x +d x y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.843
20453	1732	\begin{align*} y^{3} x^{4}+y+\left (x^{5} y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.845
20454	9789	\begin{align*} y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	5.845
20455	25773	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	5.846
20456	4530	\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \operatorname {Heaviside}\left (-2+t \right ) t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.847
20457	17349	\begin{align*} y^{\prime }&=-\frac {y}{-2+t} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.848
20458	13898	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y&=0 \\ \end{align*}	✓	✓	✓	✗	5.849
20459	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*}	✓	✓	✓	✗	5.850
20460	14703	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.853
20461	6320	\begin{align*} y^{\prime \prime }&=\operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	5.855
20462	14365	\begin{align*} x^{\prime \prime }-4 x&=1-\operatorname {Heaviside}\left (t -1\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.856
20463	17578	\begin{align*} 2 y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.857
20464	15355	\begin{align*} y^{2} y^{\prime } x&=x^{3}+y^{3} \\ \end{align*}	✓	✓	✓	✓	5.858
20465	25865	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) x&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.858
20466	5601	\begin{align*} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a&=0 \\ \end{align*}	✓	✓	✓	✗	5.859
20467	7709	\begin{align*} x^{3}+\left (1+y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.859
20468	17316	\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	5.859
20469	22371	\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}	✓	✓	✓	✓	5.861
20470	2324	\begin{align*} \sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.863
20471	25774	\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}	✗	✗	✗	✗	5.863
20472	17335	\begin{align*} y&=y^{\prime } t +3 {y^{\prime }}^{4} \\ \end{align*}	✓	✓	✓	✗	5.864
20473	22608	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	5.865
20474	4823	\begin{align*} y^{\prime } x +x +\tan \left (x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.868
20475	11356	\begin{align*} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\ \end{align*}	✗	✗	✗	✗	5.871
20476	23931	\begin{align*} y^{\prime \prime }+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.871
20477	19927	\begin{align*} \cos \left (x \right )^{2} y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.875
20478	8729	\begin{align*} x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.877
20479	25706	\begin{align*} y^{\prime } x&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.878
20480	19384	\begin{align*} \cos \left (x +y\right )&=x \sin \left (x +y\right )+x \sin \left (x +y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.881
20481	3326	\begin{align*} y&=y^{\prime } x -\sqrt {y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	5.884
20482	17945	\begin{align*} y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.884
20483	2495	\begin{align*} \sqrt {1+y^{2}}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	5.888
20484	12216	\begin{align*} y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\ \end{align*}	✓	✓	✓	✗	5.888
20485	14062	\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✗	5.892
20486	4704	\begin{align*} y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\ \end{align*}	✓	✓	✓	✓	5.895
20487	6299	\begin{align*} y^{\prime \prime }&=6 y^{2} \\ \end{align*}	✓	✓	✓	✓	5.897
20488	2849	\begin{align*} y+3+\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.901
20489	4259	\begin{align*} 1&=\frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.901
20490	5434	\begin{align*} {y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✗	5.909
20491	14503	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\ r \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.910
20492	24206	\begin{align*} y \,{\mathrm e}^{y x}-2 y^{3}+\left (x \,{\mathrm e}^{y x}-6 x y^{2}-2 y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	5.912
20493	7003	\begin{align*} y^{\prime } x +y&=x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	5.913
20494	7194	\begin{align*} 2 \left (1-x \right ) x y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.920
20495	7521	\begin{align*} y^{\prime }&=\frac {2 y}{x}+\cos \left (\frac {y}{x^{2}}\right ) \\ \end{align*}	✓	✓	✓	✗	5.920
20496	15951	\begin{align*} y^{\prime }&=3+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.920
20497	16374	\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.921
20498	11416	\begin{align*} y^{\prime } x -{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\ \end{align*}	✓	✓	✓	✗	5.925
20499	20728	\begin{align*} x y \left (-y^{\prime } x +y\right )&=x +y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.925
20500	2936	\begin{align*} y^{\prime } x +\ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.926