2.3.177 Problems 17601 to 17700

Table 2.927: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17601	15920	\begin{align*} y^{\prime }-\frac {2 y}{t}&=t^{3} {\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.891
17602	25893	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.891
17603	7383	\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{x +y}}{x^{2}+2} \\ \end{align*}	✓	✓	✓	✓	2.892
17604	24996	\begin{align*} y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.892
17605	14946	\begin{align*} x^{\prime \prime }+\omega ^{2} x&=\cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.893
17606	17613	\begin{align*} 5 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.894
17607	19252	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	2.894
17608	22807	\begin{align*} y^{\prime \prime }&=f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.895
17609	4734	\begin{align*} y^{\prime }&=x +{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	2.898
17610	23740	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	2.898
17611	5934	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.899
17612	6525	\begin{align*} 3 x y^{2}+6 x^{2} y y^{\prime }+x^{3} {y^{\prime }}^{2}+x^{3} y y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✗	2.899
17613	23176	\begin{align*} y^{\prime }&=\left (1-y\right ) \left (\frac {1}{t}-\frac {1}{10}+\frac {y}{10}\right ) \\ \end{align*}	✓	✓	✓	✓	2.899
17614	5978	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.900
17615	7791	\begin{align*} y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.901
17616	20721	\begin{align*} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.901
17617	24120	\begin{align*} \left (1-x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.901
17618	5397	\begin{align*} {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.902
17619	6175	\begin{align*} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.902
17620	6220	\begin{align*} 2 \left (1+3 x \right ) y+2 x \left (3 x +2\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.902
17621	6391	\begin{align*} \left (a +1\right ) x y^{\prime }+x^{2} y^{\prime \prime }&=x^{k} f \left (x^{k} y, k y+x y^{\prime }\right ) \\ \end{align*}	✗	✗	✗	✗	2.902
17622	14971	\begin{align*} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \\ z \left (1\right ) &= 2 \\ z^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.902
17623	19142	\begin{align*} {y^{\prime \prime \prime }}^{2}+x^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.902
17624	701	\begin{align*} y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.903
17625	5926	\begin{align*} -\left (-x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.903
17626	16376	\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}	✓	✓	✓	✓	2.904
17627	17796	\begin{align*} 4 x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.904
17628	18619	\begin{align*} x y^{\prime }+\left (x +1\right ) y&=x \\ \end{align*}	✓	✓	✓	✓	2.904
17629	3459	\begin{align*} y \left (2 x^{2} y^{2}+1\right ) y^{\prime }+x \left (1+y^{4}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.905
17630	7941	\begin{align*} y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.905
17631	23971	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	2.905
17632	1642	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ \end{align*}	✓	✓	✓	✓	2.908
17633	4866	\begin{align*} x^{2} y^{\prime }&=a +b x +c \,x^{2}-y x \\ \end{align*}	✓	✓	✓	✓	2.908
17634	15282	\begin{align*} x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.908
17635	17930	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.909
17636	24383	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	2.909
17637	16600	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=22 x +24 \\ \end{align*}	✓	✓	✓	✓	2.910
17638	23672	\begin{align*} x^{2} y^{\prime \prime }-\left (x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.911
17639	1209	\begin{align*} \left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.912
17640	15818	\begin{align*} y^{\prime }&=\left (t +1\right ) y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.912
17641	23346	\begin{align*} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -6 \sqrt {3} \\ \end{align*}	✓	✓	✓	✓	2.913
17642	22297	\begin{align*} y^{\prime }+y&=x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.914
17643	8308	\begin{align*} y^{\prime }&=x +y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.915
17644	24964	\begin{align*} y^{\prime }&=4 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.915
17645	13106	\begin{align*} a x^{\prime }&=b c \left (y-z\right ) \\ b y^{\prime }&=c a \left (-x+z\right ) \\ c z^{\prime }&=a b \left (x-y\right ) \\ \end{align*}	✓	✓	✓	✓	2.916
17646	11358	\begin{align*} y^{\prime }-\sqrt {{| y|}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.917
17647	17029	\begin{align*} 2 y+y^{\prime }&=x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.917
17648	17041	\begin{align*} y^{\prime }&=6 y^{{2}/{3}} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.917
17649	772	\begin{align*} x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.918
17650	3315	\begin{align*} x&=y y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.918
17651	9344	\begin{align*} y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.918
17652	20716	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\ \end{align*}	✓	✓	✓	✓	2.918
17653	9647	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.919
17654	26424	\begin{align*} y^{\prime \prime } \left (1+2 \ln \left (y^{\prime }\right )\right )&=1 \\ \end{align*}	✓	✓	✓	✓	2.919
17655	11515	\begin{align*} \left (y-x^{2}\right ) y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	2.920
17656	3251	\begin{align*} y^{\prime \prime }&={y^{\prime }}^{3}+y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.921
17657	3683	\begin{align*} y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.921
17658	11601	\begin{align*} \left (a +x^{2}+y^{2}\right ) y y^{\prime }+x \left (y^{2}+x^{2}-a \right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.921
17659	16800	\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.921
17660	25290	\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \\ y \left (\pi \right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.921
17661	26089	\begin{align*} x y^{2}+x^{2} y y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.921
17662	19198	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✓	2.922
17663	68	\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	2.923
17664	8882	\begin{align*} x^{2} y^{\prime }+2 y x&=1 \\ \end{align*}	✓	✓	✓	✓	2.923
17665	15946	\begin{align*} y^{\prime }&=y t \\ \end{align*}	✓	✓	✓	✓	2.923
17666	21408	\begin{align*} 2 y+y^{\prime }&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.923
17667	24818	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.923
17668	18537	\begin{align*} y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.924
17669	21400	\begin{align*} y^{\prime }+\tan \left (\theta \right ) y&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.925
17670	25223	\begin{align*} 2 t^{2} y^{\prime \prime }-5 t y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.925
17671	1572	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 y x&=x \left (x^{2}-1\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.927
17672	2835	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.927
17673	7389	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\ \end{align*}	✓	✓	✓	✓	2.927
17674	26209	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.927
17675	3538	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\ \end{align*}	✓	✓	✓	✓	2.928
17676	4640	\begin{align*} y^{\prime }&=\cos \left (x \right )-y \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.928
17677	15931	\begin{align*} y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.928
17678	18012	\begin{align*} y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	2.928
17679	4610	\begin{align*} y^{\prime }&=x^{2}+3 \cosh \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	2.929
17680	8472	\begin{align*} x y^{\prime }-4 y&=x^{6} {\mathrm e}^{x} \\ y \left (x_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	2.930
17681	13068	\begin{align*} x^{\prime }&=a_{1} x+b_{1} y+c_{1} \\ y^{\prime }&=a_{2} x+b_{2} y+c_{2} \\ \end{align*}	✓	✓	✓	✓	2.930
17682	3518	\begin{align*} y-\left (x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.931
17683	8138	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.931
17684	15873	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ w \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.931
17685	21967	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.931
17686	25052	\begin{align*} y^{\prime }&=a y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.931
17687	25232	\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.931
17688	2539	\begin{align*} y^{\prime }&=\frac {t^{2}+y^{2}}{1+t +y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.932
17689	19172	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.932
17690	26884	\begin{align*} y^{\prime }+\frac {5 y}{9 x}&=3 x^{3}+x \\ y \left (-1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.932
17691	27407	\begin{align*} x y^{\prime }+x^{2}+y x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.932
17692	11854	\begin{align*} {y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.933
17693	15924	\begin{align*} y^{\prime }&=-2 y t +4 \,{\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.934
17694	26354	\begin{align*} x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.934
17695	4011	\begin{align*} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.935
17696	24231	\begin{align*} y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.935
17697	7926	\begin{align*} y \left (1+y^{2}\right )&=2 \left (1-2 x y^{2}\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.936
17698	10429	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.937
17699	20499	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	2.937
17700	24134	\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.937