2.3.205 Problems 20401 to 20500

Table 2.983: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20401	14719	\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	4.665
20402	18595	\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}	✓	✓	✓	✓	4.665
20403	21008	\begin{align*} x^{\prime }-2 x \cos \left (t \right )&=\cos \left (t \right ) \\ x \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.665
20404	1704	\begin{align*} 3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.667
20405	2305	\begin{align*} \sqrt {t^{2}+1}\, y+y^{\prime }&=0 \\ y \left (0\right ) &= \sqrt {5} \\ \end{align*}	✓	✓	✓	✓	4.667
20406	16308	\begin{align*} y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	4.667
20407	18587	\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}	✓	✓	✓	✓	4.667
20408	26908	\begin{align*} x^{2} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	4.668
20409	699	\begin{align*} \tan \left (x \right ) y^{\prime }&=y \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	4.671
20410	3452	\begin{align*} y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \\ y \left (\frac {\pi }{8}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.671
20411	26190	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✗	4.671
20412	676	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	4.672
20413	3457	\begin{align*} \frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	4.672
20414	11366	\begin{align*} y^{\prime }-\sqrt {\frac {y^{3}+1}{x^{3}+1}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.672
20415	15232	\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.673
20416	19292	\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\ \end{align*}	✓	✓	✓	✓	4.673
20417	1713	\begin{align*} 3 x^{2} y+2 x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.676
20418	5730	\begin{align*} y^{\prime \prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.677
20419	11429	\begin{align*} 2 x y^{\prime }-y-2 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	4.679
20420	18104	\begin{align*} y^{\prime \prime }&=\sqrt {1-{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	4.682
20421	93	\begin{align*} x y^{\prime }&=3 y+x^{4} \cos \left (x \right ) \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.684
20422	14970	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.684
20423	2493	\begin{align*} t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.688
20424	11545	\begin{align*} \left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.688
20425	13991	\begin{align*} x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	4.688
20426	5973	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=x^{2} \left (x +3\right ) \\ \end{align*}	✓	✓	✓	✓	4.690
20427	14259	\begin{align*} R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \\ R \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.690
20428	27290	\begin{align*} x^{2} y^{\prime }+y x +x^{2} y^{2}&=4 \\ \end{align*}	✓	✓	✓	✓	4.691
20429	4360	\begin{align*} 1-\left (y-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.692
20430	24222	\begin{align*} x^{4} y^{\prime }&=-x^{3} y-\csc \left (y x \right ) \\ \end{align*}	✓	✓	✓	✗	4.692
20431	3467	\begin{align*} y^{\prime }&=\frac {1}{x +2 y+1} \\ \end{align*}	✓	✓	✓	✓	4.693
20432	11344	\begin{align*} y^{\prime }-x \left (x +2\right ) y^{3}-y^{2} \left (x +3\right )&=0 \\ \end{align*}	✗	✓	✓	✗	4.694
20433	13667	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b c x \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.694
20434	21432	\begin{align*} y^{\prime }+q \left (x \right ) y&=0 \\ y \left (\textit {x\_0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	4.694
20435	13317	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+b^{2} a \\ \end{align*}	✓	✓	✓	✗	4.696
20436	15775	\begin{align*} y^{\prime }&=y^{2} t^{2} \\ \end{align*}	✓	✓	✓	✓	4.696
20437	20229	\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.696
20438	781	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.697
20439	7513	\begin{align*} x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\ \end{align*}	✓	✓	✓	✓	4.698
20440	13229	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y+a \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	4.699
20441	4208	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }+y&=2 x \\ \end{align*}	✓	✓	✓	✓	4.701
20442	8503	\begin{align*} \left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.702
20443	2930	\begin{align*} 2 y \sin \left (y x \right )+\left (2 x \sin \left (y x \right )+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.704
20444	23950	\begin{align*} 1+\left (1-3 x +y\right ) y^{\prime }&=0 \\ y \left (4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.704
20445	23956	\begin{align*} y^{\prime }&=\sin \left (y\right )^{3} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.708
20446	5761	\begin{align*} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.709
20447	21477	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.709
20448	27308	\begin{align*} \frac {x}{\sin \left (y\right )}+2+\frac {\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }}{-1+\cos \left (2 y\right )}&=0 \\ \end{align*}	✓	✓	✓	✓	4.710
20449	5463	\begin{align*} {y^{\prime }}^{2} x +y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	4.711
20450	16368	\begin{align*} y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.711
20451	26340	\begin{align*} x +\sin \left (x \right )+\sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.711
20452	4256	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.712
20453	13960	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.713
20454	4353	\begin{align*} x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	4.714
20455	7682	\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	4.714
20456	26173	\begin{align*} x y^{\prime }+x \ln \left (y\right ) y^{\prime }&=x \sin \left (x \right )+\ln \left (y\right ) y \\ \end{align*}	✓	✓	✓	✗	4.714
20457	14746	\begin{align*} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	4.716
20458	2848	\begin{align*} \tan \left (x \right ) y^{\prime }-y&=1 \\ \end{align*}	✓	✓	✓	✓	4.717
20459	9923	\begin{align*} x y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.717
20460	12059	\begin{align*} y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )} \\ \end{align*}	✓	✓	✓	✓	4.717
20461	15657	\begin{align*} \sqrt {1-x}\, y^{\prime \prime }-4 y&=\sin \left (x \right ) \\ y \left (-2\right ) &= 3 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✗	✓	✗	✗	4.717
20462	23913	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=\cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.717
20463	11393	\begin{align*} x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	4.718
20464	18364	\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.718
20465	4205	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.719
20466	6598	\begin{align*} f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime }&={y^{\prime }}^{2}-y y^{\prime \prime } \\ \end{align*}	✓	✓	✗	✗	4.719
20467	17235	\begin{align*} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	4.719
20468	12543	\begin{align*} 4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.722
20469	4410	\begin{align*} {\mathrm e}^{x}+3 y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.724
20470	7951	\begin{align*} {y^{\prime }}^{2} x -y y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.724
20471	12674	\begin{align*} y^{\prime \prime }&=\frac {y}{1+{\mathrm e}^{x}} \\ \end{align*}	✗	✓	✓	✗	4.729
20472	26040	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.729
20473	14071	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✗	4.730
20474	2989	\begin{align*} \csc \left (y\right ) \cot \left (y\right ) y^{\prime }&=\csc \left (y\right )+{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.731
20475	16380	\begin{align*} x \left (-2 y+1\right )+\left (y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.731
20476	15962	\begin{align*} y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.732
20477	11337	\begin{align*} y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.733
20478	3492	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	4.734
20479	9084	\begin{align*} y^{\prime }+y \tan \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.736
20480	4678	\begin{align*} y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.739
20481	7433	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-x^{2} y&=\left (x +1\right ) \sqrt {-x^{2}+1} \\ \end{align*}	✓	✓	✓	✗	4.739
20482	13244	\begin{align*} x y^{\prime }&=x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \\ \end{align*}	✓	✓	✓	✗	4.739
20483	25701	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.739
20484	8500	\begin{align*} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.740
20485	14501	\begin{align*} {\mathrm e}^{x} \left (y-3 \left (1+{\mathrm e}^{x}\right )^{2}\right )+\left (1+{\mathrm e}^{x}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.740
20486	16200	\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}	✓	✓	✓	✓	4.740
20487	22552	\begin{align*} i^{\prime }+i&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	4.741
20488	5540	\begin{align*} x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.743
20489	6803	\begin{align*} 2 y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.744
20490	25515	\begin{align*} m y^{\prime \prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	4.746
20491	15792	\begin{align*} y^{\prime }&=y^{2}-4 \\ \end{align*}	✓	✓	✓	✓	4.747
20492	4281	\begin{align*} \left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x}&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✗	4.748
20493	18947	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.748
20494	8265	\begin{align*} 3 x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.749
20495	22517	\begin{align*} y x +x^{2} y^{\prime }&=x +1 \\ \end{align*}	✓	✓	✓	✓	4.749
20496	7382	\begin{align*} s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \\ \end{align*}	✗	✗	✓	✗	4.750
20497	15247	\begin{align*} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \\ Q \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.750
20498	23124	\begin{align*} y^{\prime }&=y^{{2}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.754
20499	14262	\begin{align*} x^{\prime }+\frac {{\mathrm e}^{-t} x}{t}&=t \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.755
20500	14274	\begin{align*} t^{3}+\frac {x}{t}+\left (x^{2}+\ln \left (t \right )\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.758