2.3.182 Problems 18101 to 18200

Table 2.895: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18101	25716	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.154
18102	56	\begin{align*} \left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.155
18103	4414	\begin{align*} y+3 x^{4} y^{2}+\left (x +2 x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.155
18104	8540	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.155
18105	17043	\begin{align*} y^{\prime }&=\tan \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.155
18106	17266	\begin{align*} \sqrt {t^{2}+1}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.155
18107	25705	\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.155
18108	25721	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.155
18109	5911	\begin{align*} n y+\left (1-x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	2.156
18110	7038	\begin{align*} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\ \end{align*}	✓	✓	✓	✓	2.156
18111	23059	\begin{align*} r r^{\prime }&=a \\ r \left (0\right ) &= b \\ \end{align*}	✓	✗	✓	✓	2.156
18112	24264	\begin{align*} L i^{\prime }+R i&=e \sin \left (t w \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.157
18113	25451	\begin{align*} y^{\prime }-\sqrt {3}\, y&=\sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.157
18114	3449	\begin{align*} y^{\prime }&=-\tan \left (t \right ) y+\sec \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.158
18115	5682	\begin{align*} 2 \sqrt {a y^{\prime }}+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.158
18116	8342	\begin{align*} y^{\prime } x&=4 y \\ \end{align*}	✓	✓	✓	✓	2.158
18117	21875	\begin{align*} y^{\prime \prime }-2 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.158
18118	12876	\begin{align*} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.159
18119	15908	\begin{align*} 3 y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.159
18120	18621	\begin{align*} \frac {\sqrt {x}\, y^{\prime }}{y}&=1 \\ \end{align*}	✓	✓	✓	✓	2.159
18121	4337	\begin{align*} x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.160
18122	7473	\begin{align*} 2 x +\frac {y}{x}+\left (y x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.160
18123	24192	\begin{align*} w^{3}+w z^{2}-z+\left (z^{3}+w^{2} z-w \right ) z^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.160
18124	2311	\begin{align*} t y+\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	2.161
18125	5881	\begin{align*} a k \,x^{-1+k} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.161
18126	6991	\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.161
18127	14357	\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.161
18128	7508	\begin{align*} y^{\prime }&=\sin \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	2.162
18129	2540	\begin{align*} y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.163
18130	33	\begin{align*} y^{\prime } y&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.164
18131	7711	\begin{align*} x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.164
18132	17473	\begin{align*} y^{\prime }-4 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	2.164
18133	3538	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \\ \end{align*}	✓	✓	✓	✓	2.165
18134	8176	\begin{align*} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	2.165
18135	11507	\begin{align*} y^{\prime } y-\sqrt {a y^{2}+b}&=0 \\ \end{align*}	✓	✓	✓	✓	2.165
18136	13230	\begin{align*} y^{\prime }&=y^{2}+a \,x^{n} y+b \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	2.165
18137	18549	\begin{align*} 2 t y+\left (-t^{2}+4\right ) y^{\prime }&=3 t^{2} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.165
18138	21615	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.165
18139	2916	\begin{align*} x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.167
18140	5707	\begin{align*} y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.167
18141	17839	\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	2.167
18142	19159	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.167
18143	15793	\begin{align*} w^{\prime }&=\frac {w}{t} \\ \end{align*}	✓	✓	✓	✓	2.168
18144	13988	\begin{align*} y^{\prime } x +\left (x +1\right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.169
18145	20677	\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.169
18146	25216	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.169
18147	785	\begin{align*} y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.170
18148	3317	\begin{align*} y&=y^{\prime } x \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.171
18149	5527	\begin{align*} a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+x^{2} a \left (-a +1\right )+y^{2}&=0 \\ \end{align*}	✓	✓	✗	✓	2.171
18150	8316	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	2.171
18151	12489	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \\ \end{align*}	✓	✓	✓	✗	2.171
18152	25754	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.171
18153	5902	\begin{align*} y+\left (-a +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	2.172
18154	24276	\begin{align*} \sin \left (\theta \right ) r^{\prime }&=-1-2 r \cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	2.172
18155	13662	\begin{align*} y^{\prime \prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	2.173
18156	22484	\begin{align*} y^{\prime } y^{\prime \prime }&=1 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.173
18157	131	\begin{align*} 3 y^{2} y^{\prime } x&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	2.174
18158	14217	\begin{align*} x^{\prime }&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.174
18159	18505	\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.174
18160	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*}	✓	✓	✓	✓	2.175
18161	49	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	2.177
18162	717	\begin{align*} y^{\prime } x -3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.177
18163	755	\begin{align*} 3 y^{2} y^{\prime } x&=3 x^{4}+y^{3} \\ \end{align*}	✓	✓	✓	✓	2.178
18164	1504	\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.178
18165	4765	\begin{align*} y^{\prime } x&=a +b \,x^{n}+c y \\ \end{align*}	✓	✓	✓	✗	2.178
18166	12417	\begin{align*} x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.178
18167	15397	\begin{align*} y^{\prime }&=\frac {2 y}{x}-\sqrt {3} \\ \end{align*}	✓	✓	✓	✓	2.178
18168	16235	\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}	✓	✓	✓	✓	2.178
18169	19704	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.178
18170	3665	\begin{align*} y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\ \end{align*}	✓	✓	✓	✓	2.179
18171	4736	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \\ \end{align*}	✓	✓	✓	✓	2.179
18172	7570	\begin{align*} m y^{\prime \prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	2.179
18173	9121	\begin{align*} y-y^{\prime } x&=y^{\prime } y^{2} {\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	2.179
18174	17154	\begin{align*} y^{\prime }+2 \cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.180
18175	22002	\begin{align*} \sin \left (x \right )+y^{\prime } y&=0 \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.180
18176	24260	\begin{align*} \left (x +a \right ) y^{\prime }&=b x +y \\ \end{align*}	✓	✓	✓	✓	2.180
18177	3645	\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}	✓	✓	✓	✓	2.181
18178	7389	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\ \end{align*}	✓	✓	✓	✓	2.181
18179	8430	\begin{align*} 4 y+y^{\prime } x&=x^{3}-x \\ \end{align*}	✓	✓	✓	✓	2.181
18180	11726	\begin{align*} x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.181
18181	14481	\begin{align*} y^{\prime }+\frac {3 y}{x}&=6 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.181
18182	22471	\begin{align*} y-x^{5} y^{4}+\left (x -x^{4} y^{5}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.181
18183	22427	\begin{align*} \cos \left (x \right ) y^{\prime }-2 y \sin \left (x \right )+3&=0 \\ \end{align*}	✓	✓	✓	✓	2.182
18184	7477	\begin{align*} x^{2} \sin \left (x \right )+4 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.183
18185	9087	\begin{align*} y^{\prime } x&=\left (-4 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.183
18186	14503	\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\ r \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.183
18187	17077	\begin{align*} 3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.183
18188	3533	\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.184
18189	15613	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	2.184
18190	15950	\begin{align*} y^{\prime }&=t +\frac {2 y}{t +1} \\ \end{align*}	✓	✓	✓	✓	2.184
18191	17058	\begin{align*} \left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	2.184
18192	19785	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.184
18193	1586	\begin{align*} \left (y-1\right )^{2} y^{\prime }&=2 x +3 \\ \end{align*}	✓	✓	✓	✓	2.185
18194	4772	\begin{align*} y^{\prime } x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.185
18195	7342	\begin{align*} y+2 x -y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.185
18196	15584	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.185
18197	21446	\begin{align*} y^{\prime }&=\frac {2 y x}{y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.185
18198	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*}	✓	✓	✓	✗	2.186
18199	14119	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y&=x \\ \end{align*}	✓	✓	✓	✗	2.186
18200	15657	\begin{align*} \sqrt {1-x}\, y^{\prime \prime }-4 y&=\sin \left (x \right ) \\ y \left (-2\right ) &= 3 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✗	✓	✗	✗	2.187