2.3.166 Problems 16501 to 16600

Table 2.905: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16501	27561	\begin{align*} y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.109
16502	25557	\begin{align*} y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\ \end{align*}	✓	✓	✓	✓	4.111
16503	11440	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\ \end{align*}	✓	✓	✓	✓	4.112
16504	6186	\begin{align*} \operatorname {a2} y+\operatorname {a1} \left (b x +a \right ) y^{\prime }+\left (b x +a \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.114
16505	12010	\begin{align*} y^{\prime }&=\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	4.114
16506	11417	\begin{align*} y^{\prime } x -y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.115
16507	19330	\begin{align*} y^{\prime } x&=y+x^{2}+9 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.115
16508	22092	\begin{align*} y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.115
16509	24102	\begin{align*} 6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.115
16510	3671	\begin{align*} y^{\prime }&=\left (9 x -y\right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.116
16511	4309	\begin{align*} x \left (1+y^{2}\right )+\left (1+2 y\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.116
16512	24701	\begin{align*} 4 y+y^{\prime \prime }&=12 \sin \left (x \right )+12 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.116
16513	20701	\begin{align*} y^{\prime \prime }+n^{2} y&=\sec \left (x n \right ) \\ \end{align*}	✓	✓	✓	✓	4.117
16514	11408	\begin{align*} y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.119
16515	25681	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.119
16516	3521	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	4.120
16517	19947	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.122
16518	11430	\begin{align*} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\ \end{align*}	✓	✓	✓	✓	4.123
16519	18812	\begin{align*} y^{\prime \prime }+2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.123
16520	1694	\begin{align*} x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.124
16521	5924	\begin{align*} \left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	4.125
16522	23687	\begin{align*} \left (x +3\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=-3\).	✓	✓	✓	✓	4.125
16523	19135	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.126
16524	19382	\begin{align*} y^{\prime } x +y&=x^{2} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.128
16525	24702	\begin{align*} 4 y+y^{\prime \prime }&=20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.128
16526	26986	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.128
16527	26093	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=x^{3} \\ \end{align*}	✓	✓	✓	✓	4.129
16528	20478	\begin{align*} 8 {y^{\prime }}^{3} x&=y \left (12 {y^{\prime }}^{2}-9\right ) \\ \end{align*}	✓	✓	✓	✗	4.131
16529	8648	\begin{align*} y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.133
16530	17124	\begin{align*} y^{\prime }&=y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.133
16531	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*}	✓	✓	✓	✓	4.135
16532	20819	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.135
16533	4861	\begin{align*} 3 y^{\prime } x&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\ \end{align*}	✓	✓	✓	✗	4.137
16534	19419	\begin{align*} x^{\prime }+x \cot \left (y \right )&=\sec \left (y \right ) \\ \end{align*}	✓	✓	✓	✓	4.137
16535	26702	\begin{align*} y^{\prime \prime } x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.137
16536	17205	\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	4.138
16537	25997	\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.138
16538	3599	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	4.139
16539	21993	\begin{align*} y^{\prime }&=5 y \\ \end{align*}	✓	✓	✓	✓	4.141
16540	25244	\begin{align*} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.141
16541	17241	\begin{align*} 2 t y+y^{2}-t^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.142
16542	27668	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-x} \cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.142
16543	9494	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.143
16544	7694	\begin{align*} y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+m y&=0 \\ \end{align*}	✗	✓	✓	✗	4.144
16545	5453	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.145
16546	23463	\begin{align*} y^{\prime \prime \prime }-y&=3 \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.145
16547	27581	\begin{align*} y^{\prime \prime }&=\left (2 y x -\frac {5}{x}\right ) y^{\prime }+4 y^{2}-\frac {4 y}{x^{2}} \\ \end{align*}	✗	✓	✓	✗	4.145
16548	5893	\begin{align*} -a^{2} x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.146
16549	10005	\begin{align*} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\ \end{align*}	✗	✗	✗	✗	4.147
16550	17084	\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.148
16551	27167	\begin{align*} x_{1}^{\prime }&=2 x_{1}+{\mathrm e}^{2 t} \cos \left (3 t \right ) \\ x_{2}^{\prime }&=6 x_{2}-4 x_{3}-2 \\ x_{3}^{\prime }&=4 x_{2}-2 x_{3}-2 \\ \end{align*}	✓	✓	✓	✓	4.148
16552	5633	\begin{align*} {y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y&=0 \\ \end{align*}	✓	✓	✗	✗	4.149
16553	11872	\begin{align*} y^{\prime }&=\frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	4.151
16554	20060	\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.151
16555	26002	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-t} \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.151
16556	7604	\begin{align*} 3 z^{\prime }+11 z&=0 \\ \end{align*}	✓	✓	✓	✓	4.152
16557	8041	\begin{align*} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✗	4.155
16558	14142	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	4.156
16559	26827	\begin{align*} x^{\prime \prime }+x&=2 \,{\mathrm e}^{t} \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.157
16560	11495	\begin{align*} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.158
16561	26439	\begin{align*} y \left (1+\ln \left (y\right )\right ) y^{\prime \prime }+{y^{\prime }}^{2}&=2 x y \,{\mathrm e}^{x^{2}} \\ \end{align*}	✗	✓	✓	✗	4.158
16562	122	\begin{align*} \left (x +y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	4.161
16563	24068	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	4.162
16564	18725	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.163
16565	17876	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.164
16566	5452	\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.165
16567	16419	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.166
16568	19134	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.166
16569	20204	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.166
16570	27152	\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }&=3 x_{1}-2 x_{2} \\ x_{3}^{\prime }&=3 x_{1}+x_{2}-3 x_{3} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 7 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.167
16571	20279	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	4.168
16572	5375	\begin{align*} {y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.169
16573	19104	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.171
16574	26242	\begin{align*} {\mathrm e}^{y^{\prime }}&=1 \\ \end{align*}	✓	✓	✓	✓	4.171
16575	19679	\begin{align*} x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.173
16576	18510	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\ \end{align*}	✓	✓	✓	✓	4.174
16577	24864	\begin{align*} {y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	4.174
16578	1153	\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.175
16579	3410	\begin{align*} y^{\prime }&=-x \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	4.177
16580	9641	\begin{align*} y+y^{\prime }&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.177
16581	19381	\begin{align*} y+x^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	4.177
16582	21259	\begin{align*} x^{\prime \prime }&=x-x^{3} \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.177
16583	4950	\begin{align*} 2 x^{2} y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	4.181
16584	16977	\begin{align*} y^{\prime }&=-\frac {2 y}{x}-3 \\ \end{align*}	✓	✓	✓	✓	4.186
16585	6015	\begin{align*} 13 y+5 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.187
16586	15723	\begin{align*} y^{\prime }+3 y&=\delta \left (x -2\right ) \\ y \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.187
16587	25174	\begin{align*} y_{1}^{\prime }&=-y_{2} \\ y_{2}^{\prime }-2 y_{2}&=y_{1} \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.187
16588	6589	\begin{align*} 4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	4.188
16589	25933	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	4.188
16590	6420	\begin{align*} y y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✗	4.189
16591	12022	\begin{align*} y^{\prime }&=\frac {x +y^{4}-2 y^{2} x^{2}+x^{4}}{y} \\ \end{align*}	✓	✓	✓	✗	4.189
16592	9328	\begin{align*} y^{\prime \prime }&=\tan \left (x \right ) \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.190
16593	6160	\begin{align*} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.191
16594	8363	\begin{align*} y^{\prime }+2 y&=1 \\ y \left (0\right ) &= {\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	4.191
16595	24099	\begin{align*} 2 y^{\prime \prime } x +y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.191
16596	5300	\begin{align*} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	4.192
16597	23234	\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.192
16598	2967	\begin{align*} y^{\prime } x&=5 y+x +1 \\ \end{align*}	✓	✓	✓	✓	4.193
16599	3576	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	4.193
16600	11357	\begin{align*} y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \\ \end{align*}	✗	✗	✗	✗	4.194