2.3.224 Problems 22301 to 22400

Table 2.1021: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22301	5313	\begin{align*} x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.978
22302	17887	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.980
22303	26690	\begin{align*} y^{\prime \prime }-\alpha ^{2} s y&=0 \\ y \left (0\right ) &= \frac {1}{s} \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.982
22304	15410	\begin{align*} y^{\prime \prime }&=9 y \\ \end{align*}	✓	✓	✓	✓	6.986
22305	6124	\begin{align*} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.987
22306	10123	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-y x -x^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	6.990
22307	12167	\begin{align*} y^{\prime }&=\frac {a^{2} x y+a +a^{2} x +a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1}{a^{2} x^{2} \left (a x y+1+a x \right )} \\ \end{align*}	✓	✓	✓	✓	6.992
22308	2540	\begin{align*} y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.994
22309	17301	\begin{align*} 1+y-t y^{\prime }&=\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	6.999
22310	16220	\begin{align*} x y y^{\prime }&=y^{2}+9 \\ \end{align*}	✓	✓	✓	✓	7.000
22311	8410	\begin{align*} u^{\prime }&=a \sqrt {1+u^{2}} \\ u \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.003
22312	11975	\begin{align*} y^{\prime }&=\frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x} \\ \end{align*}	✗	✓	✓	✗	7.003
22313	24133	\begin{align*} x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.005
22314	23859	\begin{align*} x y y^{\prime }+x^{6}-2 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.008
22315	5991	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=4 x^{3} \\ \end{align*}	✓	✓	✓	✓	7.009
22316	12573	\begin{align*} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \\ \end{align*}	✓	✓	✓	✓	7.010
22317	9528	\begin{align*} x \left (x +3\right )^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.011
22318	26206	\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.013
22319	26907	\begin{align*} y^{\prime }+\frac {y}{x}&=\frac {1}{x^{4} y^{{3}/{4}}} \\ \end{align*}	✓	✓	✓	✗	7.013
22320	4881	\begin{align*} x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	7.020
22321	20214	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	7.020
22322	6433	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	7.023
22323	25706	\begin{align*} x y^{\prime }&=2 y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.024
22324	14222	\begin{align*} R^{\prime }&=\left (t +1\right ) \left (1+R^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	7.027
22325	1801	\begin{align*} \left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \\ \end{align*}	✓	✓	✓	✓	7.031
22326	17880	\begin{align*} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.031
22327	5227	\begin{align*} \left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \\ \end{align*}	✓	✓	✓	✓	7.032
22328	22439	\begin{align*} i^{\prime }&=\frac {t -i t}{t^{2}+1} \\ i \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.033
22329	8666	\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}	✓	✓	✓	✓	7.037
22330	9941	\begin{align*} x y^{\prime \prime }+x y^{\prime }+\left (x^{4}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.037
22331	5335	\begin{align*} \left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	7.042
22332	18586	\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.042
22333	4390	\begin{align*} 2 x y^{\prime }-y&=y^{\prime } \ln \left (y y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	7.044
22334	21070	\begin{align*} y-x^{{1}/{3}}+\left (x +y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.044
22335	26608	\begin{align*} y^{\prime \prime }-y&=-2 \cos \left (x \right ) \\ y \left (\infty \right ) &= y_{0} \\ \end{align*}	✗	✓	✗	✓	7.044
22336	22362	\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.045
22337	11573	\begin{align*} \left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	7.046
22338	25789	\begin{align*} y^{\prime }&=\frac {1}{y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.046
22339	12040	\begin{align*} y^{\prime }&=\frac {\left (2 x +2+x^{3} y\right ) y}{\left (-1+2 x +\ln \left (y\right )\right ) \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	7.050
22340	9160	\begin{align*} 2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.053
22341	9328	\begin{align*} y^{\prime \prime }&=\tan \left (x \right ) \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	7.053
22342	21604	\begin{align*} \sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	7.054
22343	15506	\begin{align*} y^{\prime }-2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	7.058
22344	24819	\begin{align*} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✗	✗	7.058
22345	22457	\begin{align*} y^{\prime }-y&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	7.062
22346	6287	\begin{align*} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.064
22347	6928	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.066
22348	26257	\begin{align*} x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	7.069
22349	12051	\begin{align*} y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y} \\ \end{align*}	✓	✓	✓	✗	7.071
22350	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 \(x=0\).	✓	✓	✓	✓	7.072
22351	18957	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	7.072
22352	6991	\begin{align*} \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	7.075
22353	3660	\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\ \end{align*}	✓	✓	✓	✓	7.078
22354	4775	\begin{align*} x y^{\prime }&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	7.079
22355	4764	\begin{align*} x y^{\prime }&=a \,x^{2}+b y \\ \end{align*}	✓	✓	✓	✓	7.083
22356	13964	\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.085
22357	14064	\begin{align*} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	7.089
22358	9049	\begin{align*} x y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	7.090
22359	6351	\begin{align*} y^{\prime \prime }&=x {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	7.092
22360	17217	\begin{align*} 3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 y t \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.092
22361	12404	\begin{align*} 4 x y^{\prime \prime }+4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.098
22362	2924	\begin{align*} \frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.102
22363	12129	\begin{align*} y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \\ \end{align*}	✗	✓	✓	✗	7.103
22364	7512	\begin{align*} y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	7.105
22365	14251	\begin{align*} x^{\prime } t&=-x+t^{2} \\ \end{align*}	✓	✓	✓	✓	7.105
22366	4798	\begin{align*} x y^{\prime }+y&=a \left (x^{2}+1\right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	7.107
22367	4395	\begin{align*} x y^{2} \left (x y^{\prime }+y\right )&=1 \\ \end{align*}	✓	✓	✓	✓	7.113
22368	19802	\begin{align*} y \sqrt {x^{2}-1}+x \sqrt {y^{2}-1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.114
22369	4963	\begin{align*} \left (b \,x^{2}+a \right ) y^{\prime }&=-A -B y^{2} \\ \end{align*}	✓	✓	✓	✓	7.116
22370	14230	\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.116
22371	16244	\begin{align*} y^{\prime }&=3 x y^{3} \\ \end{align*}	✓	✓	✓	✓	7.119
22372	20285	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	7.120
22373	21456	\begin{align*} y^{\prime }+y&=x y^{3} \\ \end{align*}	✓	✓	✓	✓	7.125
22374	22092	\begin{align*} y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.129
22375	747	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{3} \\ \end{align*}	✓	✓	✓	✓	7.131
22376	7336	\begin{align*} 2 x -y \sin \left (2 x \right )&=\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	7.132
22377	12001	\begin{align*} y^{\prime }&=\frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \\ \end{align*}	✓	✓	✓	✓	7.140
22378	5143	\begin{align*} x \left (y+a \right ) y^{\prime }&=y \left (B x +A \right ) \\ \end{align*}	✓	✓	✓	✓	7.142
22379	145	\begin{align*} \frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	7.143
22380	19132	\begin{align*} y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✓	7.143
22381	20833	\begin{align*} y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.146
22382	21633	\begin{align*} \left (x -1\right ) y^{\prime \prime }+x y^{\prime }+\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.148
22383	15566	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	7.150
22384	13683	\begin{align*} y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.151
22385	19951	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	7.151
22386	21035	\begin{align*} x^{\prime }&=x^{p} \\ \end{align*}	✓	✓	✓	✓	7.151
22387	24971	\begin{align*} -y+y^{\prime }&=y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.153
22388	8743	\begin{align*} \frac {2 x y y^{\prime }}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\ \end{align*}	✓	✓	✓	✗	7.154
22389	12330	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.157
22390	27215	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.161
22391	25012	\begin{align*} y+y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.162
22392	12365	\begin{align*} x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.163
22393	5027	\begin{align*} y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.166
22394	15535	\begin{align*} y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	7.168
22395	14441	\begin{align*} 2 y x +1+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.169
22396	5086	\begin{align*} 2 \left (x +y\right ) y^{\prime }+x^{2}+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	7.171
22397	14890	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	7.172
22398	23945	\begin{align*} y^{\prime }&=\frac {1}{x^{5}+y x} \\ \end{align*}	✓	✓	✓	✓	7.172
22399	5183	\begin{align*} x \left (y x +2\right ) y^{\prime }&=3+2 x^{3}-2 y-x y^{2} \\ \end{align*}	✓	✓	✓	✗	7.175
22400	4681	\begin{align*} y^{\prime }&=x^{n} \left (a +b y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	7.178