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	7742	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.125
17602	3525	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.126
17603	12456	\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.126
17604	27187	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{3} \\ x_{2}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{1}-x_{2} \\ \end{align*}	✓	✓	✓	✓	5.127
17605	5051	\begin{align*} \left (1+y\right ) y^{\prime }&=x^{2} \left (1-y\right ) \\ \end{align*}	✓	✓	✓	✓	5.131
17606	6868	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-2 a} \\ \end{align*}	✓	✓	✓	✗	5.131
17607	13355	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b \\ \end{align*}	✓	✗	✗	✗	5.131
17608	11403	\begin{align*} y^{\prime } x +x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.132
17609	10409	\begin{align*} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.133
17610	17952	\begin{align*} \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=-\sin \left (2 x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.133
17611	19728	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	5.133
17612	25784	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	5.136
17613	8299	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	5.137
17614	21856	\begin{align*} x y^{2} {y^{\prime }}^{2}+\left (x^{3}+x y^{2}-y^{3}\right ) y^{\prime }+x^{3}-y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.137
17615	5434	\begin{align*} {y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \\ \end{align*}	✓	✓	✓	✗	5.138
17616	5480	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	5.138
17617	25529	\begin{align*} y^{\prime \prime }&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.138
17618	14504	\begin{align*} x^{\prime }-x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.141
17619	17209	\begin{align*} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.141
17620	25293	\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✓	5.144
17621	21467	\begin{align*} y^{\prime }&=-2+3 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	5.145
17622	19362	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.148
17623	11958	\begin{align*} y^{\prime }&=\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	5.149
17624	14491	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.151
17625	59	\begin{align*} y^{\prime }&={\mathrm e}^{x} y \\ y \left (0\right ) &= 2 \,{\mathrm e} \\ \end{align*}	✓	✓	✓	✓	5.152
17626	26535	\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=a \sin \left (x n +\alpha \right ) \\ \end{align*}	✓	✓	✓	✓	5.152
17627	21834	\begin{align*} 2+3 x -5 y+7 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.153
17628	17880	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.154
17629	4683	\begin{align*} y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	5.155
17630	11865	\begin{align*} y^{\prime }&=\frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \\ \end{align*}	✗	✓	✓	✗	5.155
17631	20411	\begin{align*} y {y^{\prime }}^{2}+2 y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	5.155
17632	14351	\begin{align*} x^{\prime }+5 x&=\operatorname {Heaviside}\left (-2+t \right ) \\ x \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.157
17633	15539	\begin{align*} y^{\prime }&=y^{2}-3 y \\ \end{align*}	✓	✓	✓	✓	5.157
17634	5612	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.159
17635	18034	\begin{align*} y&={y^{\prime }}^{2}-y^{\prime } x +x \\ \end{align*}	✓	✓	✓	✗	5.159
17636	26507	\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }&=x \,{\mathrm e}^{\frac {3 x}{4}} \\ \end{align*}	✓	✓	✓	✓	5.160
17637	27413	\begin{align*} {y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.160
17638	23678	\begin{align*} -a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	5.163
17639	15725	\begin{align*} y^{\prime \prime }+9 y&=\delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.164
17640	7357	\begin{align*} -y+y^{\prime } x&=x^{2} \\ y \left (2\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	5.167
17641	17847	\begin{align*} y^{\prime }&=\sin \left (y x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	5.167
17642	26974	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=3 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	5.167
17643	13206	\begin{align*} y^{\prime }&=f \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	5.168
17644	25951	\begin{align*} y^{\prime \prime }+y&=x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.169
17645	26812	\begin{align*} x^{\prime }+3 x&={\mathrm e}^{-2 t} \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.171
17646	12937	\begin{align*} y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.175
17647	25950	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{2 x}+3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.175
17648	26815	\begin{align*} x^{\prime }+x&=2 \sin \left (t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.175
17649	12252	\begin{align*} y^{\prime }&=\frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{-x^{2}+y} \\ \end{align*}	✓	✓	✓	✓	5.176
17650	11980	\begin{align*} y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\ \end{align*}	✓	✓	✓	✗	5.177
17651	6202	\begin{align*} y a \,x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.178
17652	19084	\begin{align*} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.178
17653	1163	\begin{align*} x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.180
17654	4657	\begin{align*} y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.185
17655	8453	\begin{align*} x \left (x +1\right ) y^{\prime }+y x&=1 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.185
17656	17945	\begin{align*} y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.188
17657	7042	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.190
17658	20842	\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	5.190
17659	16232	\begin{align*} y^{\prime }&={\mathrm e}^{x +y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.192
17660	20546	\begin{align*} y^{\prime \prime }+\frac {a^{2}}{y}&=0 \\ \end{align*}	✓	✓	✓	✗	5.193
17661	20725	\begin{align*} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.194
17662	25831	\begin{align*} y^{\prime }&=2 x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.194
17663	12606	\begin{align*} y^{\prime \prime }&=-\frac {\left (x^{2} a \left (1-a \right )-b \left (x +b \right )\right ) y}{x^{4}} \\ \end{align*}	✗	✓	✓	✗	5.195
17664	4967	\begin{align*} x^{3} y^{\prime }&=b \,x^{2} y+a \\ \end{align*}	✓	✓	✓	✓	5.197
17665	8462	\begin{align*} y^{\prime }-2 y x&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.198
17666	21172	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=t \\ \end{align*}	✓	✓	✓	✓	5.198
17667	126	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{4} \\ \end{align*}	✓	✓	✓	✓	5.200
17668	12254	\begin{align*} y^{\prime }&=y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6}+2 x \\ \end{align*}	✓	✓	✓	✓	5.200
17669	8251	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	5.201
17670	8298	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.201
17671	21448	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.201
17672	25286	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✓	5.201
17673	9145	\begin{align*} \frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.204
17674	19089	\begin{align*} y^{\prime } x -3 y+y^{2}&=4 x^{2}-4 x \\ \end{align*}	✓	✓	✓	✓	5.204
17675	11359	\begin{align*} y^{\prime }-a \sqrt {y}-b x&=0 \\ \end{align*}	✓	✓	✓	✗	5.207
17676	14372	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.208
17677	4210	\begin{align*} \sqrt {\left (a +x \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \\ \end{align*}	✓	✓	✓	✗	5.209
17678	13885	\begin{align*} \left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y&=0 \\ \end{align*}	✓	✓	✓	✗	5.209
17679	11671	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	5.211
17680	11690	\begin{align*} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	5.212
17681	15716	\begin{align*} 2 y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.213
17682	20462	\begin{align*} x {y^{\prime }}^{2}-\left (x -a \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.213
17683	26973	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=8 x^{2}+2 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	5.214
17684	26611	\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \\ y \left (\infty \right ) &= -{\frac {1}{5}} \\ \end{align*}	✓	✓	✓	✓	5.215
17685	1214	\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.216
17686	16975	\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	5.217
17687	17904	\begin{align*} x^{3} y^{\prime }-\sin \left (y\right )&=1 \\ y \left (\infty \right ) &= 5 \pi \\ \end{align*}	✓	✓	✗	✗	5.217
17688	3534	\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \\ \end{align*}	✓	✓	✓	✓	5.218
17689	5473	\begin{align*} x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.220
17690	8209	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	5.221
17691	9519	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.221
17692	16812	\begin{align*} y^{\prime \prime }-16 y&=\delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	5.222
17693	19172	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	5.222
17694	7703	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.223
17695	7124	\begin{align*} \left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	5.224
17696	19736	\begin{align*} \theta ^{\prime \prime }&=-p^{2} \theta \\ \end{align*}	✓	✓	✓	✓	5.224
17697	7436	\begin{align*} t^{2} x^{\prime }+3 t x&=t^{4} \ln \left (t \right )+1 \\ x \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.226
17698	20543	\begin{align*} y^{\prime \prime }&=y \\ \end{align*}	✓	✓	✓	✓	5.227
17699	23316	\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.227
17700	770	\begin{align*} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.228