2.3.177 Problems 17601 to 17700

Table 2.897: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17601	19794	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	3.128
17602	5493	\begin{align*} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6}&=0 \\ \end{align*}	✓	✓	✓	✓	3.129
17603	8502	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.129
17604	8878	\begin{align*} y^{\prime }+{\mathrm e}^{x} y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.129
17605	15774	\begin{align*} y^{\prime }&=\frac {1+y}{1+t} \\ \end{align*}	✓	✓	✓	✓	3.129
17606	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*}	✗	✓	✗	✗	3.130
17607	19789	\begin{align*} y^{\prime }+\frac {y}{x}&=-x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	3.130
17608	22324	\begin{align*} y^{\prime }&=\sec \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.130
17609	23401	\begin{align*} \left (2+x \right ) y^{\prime \prime }-y^{\prime }+\frac {y}{2+x}&=0 \\ \end{align*}	✓	✓	✓	✗	3.131
17610	2481	\begin{align*} y^{\prime }-2 t y&=t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.133
17611	7933	\begin{align*} 2 x y^{5}-y+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.133
17612	25204	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ \end{align*}	✓	✓	✓	✓	3.134
17613	7908	\begin{align*} 1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.135
17614	8213	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.135
17615	15457	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.136
17616	2318	\begin{align*} y^{\prime }&=\left (1+t \right ) \left (1+y\right ) \\ \end{align*}	✓	✓	✓	✓	3.137
17617	25792	\begin{align*} y^{\prime }&=\frac {x^{2}}{5}+y \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.137
17618	19985	\begin{align*} y&=y {y^{\prime }}^{2}+2 y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	3.138
17619	15800	\begin{align*} y^{\prime }&=\frac {t}{y-t^{2} y} \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.141
17620	2071	\begin{align*} x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.145
17621	2077	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.145
17622	4727	\begin{align*} y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.145
17623	15907	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.145
17624	16600	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=22 x +24 \\ \end{align*}	✓	✓	✓	✓	3.145
17625	16592	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=10 x +12 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.147
17626	4996	\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	3.149
17627	11879	\begin{align*} y^{\prime }&=\frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x} \\ \end{align*}	✓	✓	✓	✗	3.149
17628	24142	\begin{align*} y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.149
17629	15491	\begin{align*} x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.151
17630	1609	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}+y}{x^{2}+y^{2}} \\ \end{align*}	✗	✗	✗	✗	3.153
17631	8210	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	3.153
17632	9553	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.153
17633	2069	\begin{align*} x \left (x +1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.154
17634	7851	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.155
17635	15546	\begin{align*} y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	3.155
17636	20271	\begin{align*} \left (x y^{2}+1+x \right ) y^{\prime }+y+y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	3.155
17637	20547	\begin{align*} y^{\prime \prime }&=y^{3}-y \\ \end{align*}	✓	✓	✓	✗	3.156
17638	9120	\begin{align*} \left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.159
17639	11639	\begin{align*} x \left (y \ln \left (y x \right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (y x \right )-y+a x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.159
17640	13682	\begin{align*} y^{\prime \prime }+a x y^{\prime }+b x y&=0 \\ \end{align*}	✗	✓	✓	✗	3.159
17641	11577	\begin{align*} 3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 \left (x +1\right ) x y-3 \,{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	3.160
17642	16697	\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.161
17643	7697	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	3.162
17644	16160	\begin{align*} y^{\prime \prime }+3 y^{\prime }+8 y&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.163
17645	2374	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t -2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.164
17646	1672	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	3.165
17647	15599	\begin{align*} y^{\prime }&=\frac {y}{x}+\sin \left (x^{2}\right ) \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.165
17648	2076	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.166
17649	7800	\begin{align*} y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\ \end{align*}	✓	✓	✓	✓	3.166
17650	4405	\begin{align*} y^{\prime }+\frac {y}{x}&={\mathrm e}^{y x} \\ \end{align*}	✓	✓	✓	✗	3.167
17651	24260	\begin{align*} \left (a +x \right ) y^{\prime }&=b x +y \\ \end{align*}	✓	✓	✓	✓	3.167
17652	21480	\begin{align*} x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.168
17653	21998	\begin{align*} \frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.169
17654	22028	\begin{align*} y+2 x y^{3}+\left (1+3 y^{2} x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.169
17655	18050	\begin{align*} y y^{\prime } x -y^{2}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.170
17656	5355	\begin{align*} {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	3.171
17657	8357	\begin{align*} y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\ \end{align*}	✓	✓	✓	✓	3.171
17658	4643	\begin{align*} y^{\prime }&=\sin \left (2 x \right )-\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.173
17659	12147	\begin{align*} y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\ \end{align*}	✓	✓	✓	✗	3.174
17660	23984	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	3.174
17661	15797	\begin{align*} y^{\prime }&=-y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.177
17662	4288	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.178
17663	13726	\begin{align*} y^{\prime \prime } x +n y^{\prime }+b \,x^{1-2 n} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.178
17664	14052	\begin{align*} x {y^{\prime }}^{2}-2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	3.178
17665	25273	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=t^{4} \\ \end{align*}	✓	✓	✓	✓	3.178
17666	724	\begin{align*} y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.179
17667	8292	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.180
17668	4742	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.181
17669	8756	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.181
17670	11439	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \\ \end{align*}	✓	✓	✓	✓	3.181
17671	15045	\begin{align*} x^{\prime }+5 x&=10 t +2 \\ x \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.181
17672	17146	\begin{align*} y^{\prime } x +y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	3.181
17673	19908	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.181
17674	4531	\begin{align*} y^{\prime \prime \prime \prime }+4 y&=\left (2 t^{2}+t +1\right ) \delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.182
17675	19353	\begin{align*} \left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.182
17676	22661	\begin{align*} u^{\prime \prime }+16 u&=0 \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.183
17677	24121	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.183
17678	4235	\begin{align*} {\mathrm e}^{y} y^{\prime }+2 x&=2 x \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.184
17679	15338	\begin{align*} \left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.184
17680	19803	\begin{align*} \left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.185
17681	14722	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=10 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	3.187
17682	71	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (a \right ) &= b \\ \end{align*}	✓	✓	✓	✗	3.188
17683	22539	\begin{align*} y^{\prime } x&=x^{3}+2 y \\ \end{align*}	✓	✓	✓	✓	3.188
17684	25712	\begin{align*} \left (y^{3}+1\right ) y^{\prime }&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.188
17685	1849	\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.189
17686	11336	\begin{align*} y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.189
17687	25856	\begin{align*} y+6 x y^{3}-4 y^{4}-\left (2 x +4 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.189
17688	2094	\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.190
17689	22558	\begin{align*} y^{\prime }&=3 x +2 y \\ \end{align*}	✓	✓	✓	✓	3.191
17690	25626	\begin{align*} \frac {c y^{\prime \prime }}{\omega ^{2}}+c y&=\cos \left (\omega t \right ) \\ \end{align*}	✓	✓	✓	✓	3.192
17691	20451	\begin{align*} y^{2} x^{2}-3 y y^{\prime } x&=2 y^{2}+x^{3} \\ \end{align*}	✓	✓	✓	✗	3.193
17692	14828	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.194
17693	11800	\begin{align*} {y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d&=0 \\ \end{align*}	✓	✓	✓	✓	3.195
17694	25441	\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.195
17695	9821	\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.197
17696	17240	\begin{align*} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.197
17697	1735	\begin{align*} 3 y^{2} x^{2}+2 y+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.198
17698	15922	\begin{align*} y^{\prime }&=\frac {y}{1+t}+4 t^{2}+4 t \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	3.198
17699	24837	\begin{align*} {y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	3.198
17700	4644	\begin{align*} y^{\prime }&=\sin \left (x \right )+2 \tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.200