2.3.182 Problems 18101 to 18200

Table 2.937: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18101	20317	\begin{align*} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\ \end{align*}	✓	✓	✓	✓	3.134
18102	25615	\begin{align*} y^{\prime }-a y&=t \\ \end{align*}	✓	✓	✓	✓	3.134
18103	5677	\begin{align*} {y^{\prime }}^{6}&=\left (y-a \right )^{4} \left (y-b \right )^{3} \\ \end{align*}	✓	✓	✓	✓	3.135
18104	7536	\begin{align*} y^{\prime }-\frac {y}{x}&=\sin \left (2 x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	3.135
18105	17173	\begin{align*} y^{\prime }-\frac {y}{t}&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.135
18106	27403	\begin{align*} x y^{\prime } \left (y^{\prime }+2\right )&=y \\ \end{align*}	✓	✓	✓	✓	3.135
18107	6053	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.136
18108	7443	\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.136
18109	27400	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) x&=2 y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.136
18110	16226	\begin{align*} y y^{\prime }&=x y^{2}+x \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.137
18111	26437	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.137
18112	20278	\begin{align*} 1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.138
18113	20544	\begin{align*} y^{3} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	3.138
18114	11634	\begin{align*} \left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✗	3.139
18115	6514	\begin{align*} x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 {y^{\prime }}^{2} x +x \left (x +2 y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.140
18116	2459	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.141
18117	6134	\begin{align*} -3 y+x y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.141
18118	24309	\begin{align*} y^{\prime }&=\cos \left (x \right )+y \tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.141
18119	27291	\begin{align*} 3 y^{\prime }+y^{2}+\frac {2}{x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	3.141
18120	49	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	3.142
18121	14705	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.142
18122	16902	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.142
18123	26686	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.142
18124	1132	\begin{align*} y^{\prime }&=\frac {3 x^{2}-1}{3+2 y} \\ \end{align*}	✓	✓	✓	✓	3.143
18125	15969	\begin{align*} y^{\prime }&=3-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	3.143
18126	19162	\begin{align*} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.144
18127	9519	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.145
18128	18542	\begin{align*} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.145
18129	23724	\begin{align*} x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.145
18130	11492	\begin{align*} x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.147
18131	2969	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.148
18132	18019	\begin{align*} y&=x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.148
18133	27205	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.148
18134	17183	\begin{align*} -\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.150
18135	728	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.151
18136	1724	\begin{align*} 2 y x +y^{2}+\left (2 y x +x^{2}-2 x^{2} y^{2}-2 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.151
18137	7754	\begin{align*} y^{\prime }+\frac {y}{x}&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.151
18138	12077	\begin{align*} y^{\prime }&=\frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}} \\ \end{align*}	✓	✓	✓	✗	3.151
18139	18940	\begin{align*} y^{\prime \prime }-y&=-20 \delta \left (-3+t \right ) \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.151
18140	22062	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.151
18141	24130	\begin{align*} x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.151
18142	20142	\begin{align*} a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.152
18143	21417	\begin{align*} {\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.152
18144	5835	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.153
18145	19390	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.153
18146	19747	\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}	✓	✓	✓	✓	3.153
18147	8733	\begin{align*} y^{\prime }&=\frac {x -2 y+5}{-4-2 x +y} \\ \end{align*}	✓	✓	✓	✓	3.155
18148	8873	\begin{align*} L y^{\prime }+R y&=E \sin \left (\omega x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.155
18149	14702	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.155
18150	15595	\begin{align*} y^{\prime }&=4 y+1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.155
18151	16284	\begin{align*} x y^{\prime }-y&=x^{2} {\mathrm e}^{-x^{2}} \\ y \left (3\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.155
18152	19928	\begin{align*} \left (x +1\right ) y^{\prime }-n y&={\mathrm e}^{x} \left (x +1\right )^{n +1} \\ \end{align*}	✓	✓	✓	✓	3.155
18153	4870	\begin{align*} x^{2} y^{\prime }+x \left (x +2\right ) y&=x \left (1-{\mathrm e}^{-2 x}\right )-2 \\ \end{align*}	✓	✓	✓	✓	3.156
18154	11614	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	3.156
18155	21626	\begin{align*} L i^{\prime }+R i&=E_{0} \\ i \left (0\right ) &= i_{0} \\ \end{align*}	✓	✓	✓	✓	3.156
18156	2088	\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.158
18157	10376	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.158
18158	15967	\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \\ \end{align*}	✓	✓	✓	✓	3.158
18159	22144	\begin{align*} y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\ \end{align*}	✓	✓	✓	✓	3.158
18160	26883	\begin{align*} y^{\prime }+\frac {2 y}{x +1}&=3 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.158
18161	16206	\begin{align*} y^{\prime }+\left (8-x \right ) y-y^{2}&=-8 x \\ \end{align*}	✓	✓	✓	✗	3.159
18162	16235	\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}	✓	✓	✓	✓	3.159
18163	26868	\begin{align*} y^{\prime }+y&={\mathrm e}^{x}-\sin \left (y\right ) \\ \end{align*}	✗	✗	✗	✗	3.159
18164	17784	\begin{align*} 5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.160
18165	1599	\begin{align*} \left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	3.161
18166	7484	\begin{align*} 2 x y^{3}+1+\left (3 x^{2} y^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.161
18167	14249	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.161
18168	19079	\begin{align*} \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )+\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.161
18169	25437	\begin{align*} y^{\prime }&=2 y+3 \cos \left (t \right )+4 \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.161
18170	12969	\begin{align*} 4 y y^{\prime \prime }-5 {y^{\prime }}^{2}+a y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.162
18171	20816	\begin{align*} x y^{\prime }-2 y&=x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.163
18172	8739	\begin{align*} y+x \left (1+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.164
18173	19348	\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.164
18174	21448	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.164
18175	3533	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.165
18176	6255	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.166
18177	21069	\begin{align*} 3 x^{2}-y+\left (4 y^{3}-x \right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	3.166
18178	27305	\begin{align*} 2 x \left (1+\sqrt {x^{2}-y}\right )-\sqrt {x^{2}-y}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.167
18179	1575	\begin{align*} {\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.168
18180	4659	\begin{align*} y^{\prime }&=x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \\ \end{align*}	✓	✓	✓	✓	3.168
18181	8172	\begin{align*} y^{\prime }+4 y x&=8 x^{3} \\ \end{align*}	✓	✓	✓	✓	3.168
18182	12112	\begin{align*} y^{\prime }&=\frac {y \left (x -y\right )}{x \left (x -y-y^{3}-y^{4}\right )} \\ \end{align*}	✓	✓	✓	✗	3.168
18183	11603	\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}	✓	✓	✓	✓	3.169
18184	1189	\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.172
18185	19773	\begin{align*} y-2 x y^{\prime }-y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.172
18186	9242	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.173
18187	13990	\begin{align*} \left (x^{3}+x \right ) y^{\prime }+4 x^{2} y&=2 \\ \end{align*}	✓	✓	✓	✓	3.173
18188	4204	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.174
18189	7439	\begin{align*} \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.174
18190	25448	\begin{align*} y^{\prime }-a y&=R \cos \left (\omega t -\phi \right ) \\ \end{align*}	✓	✓	✓	✓	3.174
18191	25753	\begin{align*} y^{\prime }+y \sin \left (x \right )&=x \\ \end{align*}	✓	✓	✓	✓	3.174
18192	17062	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.175
18193	21669	\begin{align*} x^{4} \left (x^{2}+1\right ) \left (x -1\right )^{2} y^{\prime \prime }+4 x^{3} \left (x -1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	3.175
18194	795	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	3.177
18195	2494	\begin{align*} y^{\prime }&=\frac {2 t}{y+t^{2} y} \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.178
18196	7246	\begin{align*} 2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.178
18197	766	\begin{align*} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.180
18198	12032	\begin{align*} y^{\prime }&=\frac {\left (x^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	3.180
18199	697	\begin{align*} y^{\prime }&=4 x^{3} y-y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	3.181
18200	14388	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-x-14 \\ \end{align*}	✓	✓	✓	✓	3.182