2.3.191 Problems 19001 to 19100

Table 2.925: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19001	15829	\begin{align*} y^{\prime }&=t^{2}+t^{2} y \\ \end{align*}	✓	✓	✓	✓	4.130
19002	19934	\begin{align*} 3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	4.130
19003	7028	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	4.131
19004	11366	\begin{align*} y^{\prime }-\sqrt {\frac {y^{3}+1}{x^{3}+1}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.131
19005	2954	\begin{align*} \left (x^{2}+y^{2}-2 y\right ) y^{\prime }&=2 x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✗	✓	✓	4.132
19006	8406	\begin{align*} y^{\prime }&=y+\frac {y}{x \ln \left (x \right )} \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.134
19007	13353	\begin{align*} y^{\prime }&=y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2} \\ \end{align*}	✓	✓	✓	✓	4.135
19008	13939	\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+\mu \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	4.135
19009	8267	\begin{align*} y^{\prime } x +y&=2 x \\ y \left (x_{0} \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.136
19010	5208	\begin{align*} y^{2} y^{\prime }+x \left (2-y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.138
19011	12173	\begin{align*} y^{\prime }&=\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	4.138
19012	13285	\begin{align*} y^{\prime }&=y^{2}+b y+a \left (\lambda -b \right ) {\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\ \end{align*}	✓	✓	✓	✗	4.138
19013	26209	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.138
19014	15953	\begin{align*} y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\ \end{align*}	✓	✓	✓	✓	4.139
19015	8742	\begin{align*} 2 y^{\prime } x +y&=y^{2} \sqrt {x -y^{2} x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.140
19016	12036	\begin{align*} y^{\prime }&=\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	4.140
19017	4720	\begin{align*} y^{\prime }&=\cot \left (x \right ) \cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.141
19018	13368	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.141
19019	24370	\begin{align*} 2 y^{2}+3 y x -2 y+6 x +x \left (x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.141
19020	6003	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=a -x +x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.143
19021	14142	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✗	4.143
19022	11506	\begin{align*} y y^{\prime }+a y^{2}-b \cos \left (x +c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.145
19023	21436	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	4.145
19024	25090	\begin{align*} y^{\prime } t +y&=\ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.146
19025	712	\begin{align*} -y+y^{\prime } x&=x \\ y \left (1\right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	4.147
19026	13308	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \\ \end{align*}	✓	✓	✓	✗	4.147
19027	23254	\begin{align*} y y^{\prime }&=3 \\ \end{align*}	✓	✓	✓	✓	4.148
19028	1186	\begin{align*} y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.149
19029	26219	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y y^{\prime }&={\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.149
19030	7005	\begin{align*} a y+y^{\prime }&=k \,{\mathrm e}^{b x} \\ \end{align*}	✓	✓	✓	✓	4.150
19031	2958	\begin{align*} y^{\prime }-y x&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.151
19032	1182	\begin{align*} y^{\prime }&=a y+b y^{2} \\ \end{align*}	✓	✓	✓	✓	4.152
19033	15954	\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	4.153
19034	1232	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }&=y-{\mathrm e}^{x} y \\ \end{align*}	✓	✓	✓	✓	4.158
19035	4584	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	4.158
19036	22032	\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	4.160
19037	14840	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	4.162
19038	4089	\begin{align*} x^{2} y^{\prime }&=\left (-1+y\right ) x +\left (-1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.163
19039	674	\begin{align*} y y^{\prime }&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.164
19040	3544	\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.164
19041	7037	\begin{align*} \left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	4.164
19042	17669	\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.165
19043	24962	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\tan \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.167
19044	14323	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	4.169
19045	19347	\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.169
19046	15063	\begin{align*} 3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.170
19047	20969	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{-y^{2}}}{y \left (x^{2}+2 x \right )} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.171
19048	24240	\begin{align*} \left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.171
19049	2306	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.175
19050	4909	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=2 x \left (x^{2}+1\right )^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	4.175
19051	5079	\begin{align*} 2 y y^{\prime }&=x y^{2}+x^{3} \\ \end{align*}	✓	✓	✓	✓	4.176
19052	17814	\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.176
19053	22950	\begin{align*} y^{\prime } \sin \left (y\right )&=\sec \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.176
19054	26204	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.176
19055	5588	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.177
19056	7007	\begin{align*} y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.177
19057	5210	\begin{align*} \left (x +y^{2}\right ) y^{\prime }+y&=b x +a \\ \end{align*}	✓	✓	✓	✗	4.178
19058	1713	\begin{align*} 3 x^{2} y+2 x^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.182
19059	11707	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	4.184
19060	4360	\begin{align*} 1-\left (y-2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.186
19061	4633	\begin{align*} y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	4.186
19062	23402	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x -1}+\frac {4 y}{\left (x -1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	4.186
19063	1690	\begin{align*} \frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.187
19064	19082	\begin{align*} \left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.188
19065	17236	\begin{align*} -2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.189
19066	9200	\begin{align*} -y+y^{\prime } x&=2 x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.190
19067	1245	\begin{align*} 3 t +2 y&=-y^{\prime } t \\ \end{align*}	✓	✓	✓	✓	4.191
19068	4867	\begin{align*} x^{2} y^{\prime }+\left (1-2 x \right ) y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	4.191
19069	17377	\begin{align*} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	4.191
19070	8372	\begin{align*} y^{\prime }&=\frac {1+3 x}{2 y} \\ y \left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.193
19071	3469	\begin{align*} y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.194
19072	22087	\begin{align*} y^{\prime }-2 y&=y x \\ \end{align*}	✓	✓	✓	✓	4.194
19073	8997	\begin{align*} 4 x^{2} y^{\prime \prime }-4 \,{\mathrm e}^{x} y^{\prime } x +3 \cos \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.195
19074	4638	\begin{align*} y^{\prime }&=\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	4.198
19075	21445	\begin{align*} y^{\prime }&=\frac {x^{4}+2 y}{x} \\ \end{align*}	✓	✓	✓	✓	4.199
19076	7573	\begin{align*} 2 y^{\prime \prime }+18 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.202
19077	16236	\begin{align*} y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.204
19078	14137	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 \sin \left (x \right ) y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✗	4.205
19079	6431	\begin{align*} y y^{\prime \prime }&=\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.207
19080	25898	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.207
19081	21024	\begin{align*} x^{\prime }&=\frac {x}{t^{2}+1} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.208
19082	9945	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.209
19083	22987	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\sec \left (x \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.209
19084	676	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	4.210
19085	20265	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.211
19086	17473	\begin{align*} y^{\prime }-4 y&=t^{2} \\ \end{align*}	✓	✓	✓	✓	4.212
19087	17933	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.213
19088	11855	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	4.214
19089	13379	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.214
19090	15658	\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right )&=x \,{\mathrm e}^{x} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✗	✗	✗	✗	4.214
19091	3452	\begin{align*} y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \\ y \left (\frac {\pi }{8}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.216
19092	4234	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.216
19093	19792	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=x^{3}-x^{2} \arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.216
19094	5486	\begin{align*} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	4.217
19095	9936	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.217
19096	5223	\begin{align*} y \left (1+y\right ) y^{\prime }&=x \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✗	4.218
19097	16230	\begin{align*} y y^{\prime }&=x y^{2}-9 x \\ \end{align*}	✓	✓	✓	✓	4.218
19098	3605	\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.222
19099	6828	\begin{align*} \sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.223
19100	15796	\begin{align*} y^{\prime }&=t y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.224