2.3.177 Problems 17601 to 17700

Table 2.885: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17601	21039	\begin{align*} x^{\prime }&=t^{2} x^{4}+1 \\ x \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	1.964
17602	1591	\begin{align*} y^{\prime }+2 x \left (1+y\right )&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.965
17603	24000	\begin{align*} y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.965
17604	9194	\begin{align*} x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	1.966
17605	19771	\begin{align*} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	1.966
17606	197	\begin{align*} 3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\ \end{align*}	✓	✓	✓	✓	1.967
17607	9095	\begin{align*} y^{2} y^{\prime }&=2+x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	1.967
17608	15720	\begin{align*} 4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.967
17609	17325	\begin{align*} t^{2}-y+\left (y-t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.967
17610	5010	\begin{align*} \sqrt {x^{2}+1}\, y^{\prime }&=2 x -y \\ \end{align*}	✓	✓	✓	✓	1.968
17611	22573	\begin{align*} y^{\prime }&=2-\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	1.968
17612	4673	\begin{align*} y^{\prime }&=f \left (x \right )+a y+b y^{2} \\ \end{align*}	✗	✗	✗	✗	1.969
17613	8451	\begin{align*} y^{\prime }+4 y x&=x^{3} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.969
17614	17644	\begin{align*} 2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.969
17615	22450	\begin{align*} y^{2}+x y^{\prime } y&=\left (2 y^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.969
17616	25440	\begin{align*} y^{\prime }-4 y&=\cos \left (3 t \right )+\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.969
17617	25673	\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.969
17618	5183	\begin{align*} x \left (y x +2\right ) y^{\prime }&=3+2 x^{3}-2 y-x y^{2} \\ \end{align*}	✓	✓	✓	✗	1.970
17619	6009	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.970
17620	15481	\begin{align*} x^{\prime \prime }&=\left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \\ \end{align*}	✓	✓	✓	✗	1.970
17621	15607	\begin{align*} \left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.970
17622	758	\begin{align*} \left ({\mathrm e}^{y}+x \right ) y^{\prime }&=x \,{\mathrm e}^{-y}-1 \\ \end{align*}	✓	✓	✓	✓	1.971
17623	4430	\begin{align*} 2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.971
17624	4608	\begin{align*} y^{\prime }&=x +\sin \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	1.971
17625	6824	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.971
17626	7028	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.971
17627	13931	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	1.972
17628	14969	\begin{align*} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x&=0 \\ x \left (1\right ) &= 2 \\ x^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.972
17629	21509	\begin{align*} y^{\prime }-y&=x \\ \end{align*}	✓	✓	✓	✓	1.972
17630	2891	\begin{align*} y^{2} \left (y^{\prime } y-x \right )+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	1.974
17631	4197	\begin{align*} y^{\prime } x +n y&=x^{n} \\ \end{align*}	✓	✓	✓	✓	1.974
17632	4757	\begin{align*} y^{\prime } x&=x^{2} \sin \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	1.974
17633	21019	\begin{align*} x^{\prime }+a x&=b t \\ x \left (t_{0} \right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✓	1.974
17634	23158	\begin{align*} y^{\prime } x +6 y&=1+3 x \\ \end{align*}	✓	✓	✓	✓	1.974
17635	25351	\begin{align*} t y^{\prime \prime }+\left (-1+t \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	1.974
17636	180	\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.975
17637	17870	\begin{align*} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	1.975
17638	22136	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	1.975
17639	25090	\begin{align*} t y^{\prime }+y&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.975
17640	1171	\begin{align*} y+\ln \left (t \right ) y^{\prime }&=\cot \left (t \right ) \\ \end{align*}	✓	✓	✓	✗	1.976
17641	23176	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (\frac {1}{t}-\frac {1}{10}+\frac {y}{10}\right ) \\ \end{align*}	✓	✓	✓	✓	1.976
17642	24471	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.976
17643	25452	\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	1.976
17644	11743	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	1.977
17645	16197	\begin{align*} y^{\prime }+3 y x&=6 x \\ \end{align*}	✓	✓	✓	✓	1.977
17646	18524	\begin{align*} t y^{\prime }+4 y&=t^{2}-t +1 \\ y \left (1\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	1.977
17647	19666	\begin{align*} x^{\prime }&=b \,{\mathrm e}^{x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.977
17648	22457	\begin{align*} y^{\prime }-y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	1.977
17649	22526	\begin{align*} x^{2}+y^{2}+\left (2 y x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.977
17650	16145	\begin{align*} y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.978
17651	17528	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+4 y&=t \\ \end{align*}	✓	✓	✓	✓	1.978
17652	5459	\begin{align*} x {y^{\prime }}^{2}-y^{\prime } y+a x&=0 \\ \end{align*}	✓	✓	✓	✓	1.979
17653	13415	\begin{align*} y^{\prime }&=y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	1.979
17654	34	\begin{align*} y^{\prime } y&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.980
17655	7332	\begin{align*} x^{2} y^{\prime }-y x&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	1.980
17656	17859	\begin{align*} y^{\prime }&=y-x^{2} \\ \end{align*}	✓	✓	✓	✓	1.980
17657	20223	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-2 y x&=-x^{3}+x \\ \end{align*}	✓	✓	✓	✓	1.980
17658	22962	\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.980
17659	709	\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	1.981
17660	3443	\begin{align*} y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.981
17661	7387	\begin{align*} x^{\prime }&=3 t^{2} x \\ \end{align*}	✓	✓	✓	✓	1.981
17662	20060	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.981
17663	3493	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y&=x^{2} \\ \end{align*}	✓	✓	✓	✗	1.982
17664	3234	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 y^{\prime } x -6 y&=\cos \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.983
17665	11304	\begin{align*} y^{\prime }+a y-c \,{\mathrm e}^{b x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.983
17666	4965	\begin{align*} x \left (a x +1\right ) y^{\prime }+a -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.984
17667	7013	\begin{align*} y^{\prime }+y \cos \left (x \right )&={\mathrm e}^{-\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	1.984
17668	13414	\begin{align*} y^{\prime }&=y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m} \\ \end{align*}	✓	✓	✓	✗	1.984
17669	18489	\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \\ y \left (0\right ) &= -7 \\ \end{align*}	✓	✓	✓	✓	1.984
17670	41	\begin{align*} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.985
17671	19491	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.985
17672	113	\begin{align*} x^{2} y^{\prime }&=y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	1.986
17673	772	\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.987
17674	5335	\begin{align*} \left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	1.987
17675	6967	\begin{align*} r^{\prime }&=\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	1.987
17676	18023	\begin{align*} y^{\prime } x -y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	1.987
17677	2312	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.988
17678	8655	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (-1+t \right )+\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.988
17679	11425	\begin{align*} y^{\prime } x -y f \left (y x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.988
17680	20406	\begin{align*} y&=\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.988
17681	20753	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \\ \end{align*}	✓	✓	✓	✗	1.989
17682	23197	\begin{align*} y-2 x -y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	1.989
17683	1222	\begin{align*} y^{\prime }&=\frac {-1-2 y x -y^{2}}{x^{2}+2 y x} \\ \end{align*}	✓	✓	✓	✗	1.990
17684	8883	\begin{align*} 2 y+y^{\prime }&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.990
17685	25055	\begin{align*} t y^{\prime }&=2 y-t \\ \end{align*}	✓	✓	✓	✓	1.990
17686	25778	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	1.990
17687	9390	\begin{align*} x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.991
17688	4764	\begin{align*} y^{\prime } x&=a \,x^{2}+b y \\ \end{align*}	✓	✓	✓	✓	1.992
17689	5371	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.992
17690	14888	\begin{align*} x^{\prime }&=t^{2} x \\ \end{align*}	✓	✓	✓	✓	1.992
17691	15901	\begin{align*} y^{\prime }&=-3 y+4 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.992
17692	16343	\begin{align*} 1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.993
17693	24251	\begin{align*} 2 x \left (y-x^{2}\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.993
17694	1408	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }&=x_{1}-x_{2} \\ x_{3}^{\prime }&=-2 x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	1.994
17695	5239	\begin{align*} 3 y^{2} y^{\prime }&=1+x +a y^{3} \\ \end{align*}	✓	✓	✓	✓	1.994
17696	7225	\begin{align*} \left (1+y\right ) y^{\prime }&=y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.994
17697	8525	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.994
17698	14766	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.994
17699	15587	\begin{align*} y^{\prime }&=y x +x \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.994
17700	18547	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.994