2.3.224 Problems 22301 to 22400

Table 2.979: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22301	5203	\begin{align*} x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\ \end{align*}	✓	✓	✓	✓	5.936
22302	17264	\begin{align*} \frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.936
22303	21720	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	5.936
22304	21338	\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.937
22305	13980	\begin{align*} x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.938
22306	7546	\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.941
22307	1582	\begin{align*} x^{2} y y^{\prime }&=\left (y^{2}-1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	5.943
22308	7486	\begin{align*} 3 y+2 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.943
22309	17975	\begin{align*} \sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.944
22310	25787	\begin{align*} y^{\prime } y&=-x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.944
22311	14887	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.947
22312	24208	\begin{align*} y \left (y^{3}-x \right )+x \left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.949
22313	14549	\begin{align*} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.951
22314	20833	\begin{align*} y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.954
22315	11809	\begin{align*} {y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.957
22316	5167	\begin{align*} x \left (x -2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.958
22317	1657	\begin{align*} y^{\prime }&=\frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \\ \end{align*}	✓	✓	✓	✗	5.960
22318	11895	\begin{align*} y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\ \end{align*}	✓	✓	✓	✗	5.960
22319	12182	\begin{align*} y^{\prime }&=\frac {-x y^{2}+x^{3}-x -y^{6}+3 x^{2} y^{4}-3 x^{4} y^{2}+x^{6}}{\left (-y^{2}+x^{2}-1\right ) y} \\ \end{align*}	✓	✓	✓	✗	5.967
22320	4860	\begin{align*} 2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	5.968
22321	4921	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\ \end{align*}	✓	✓	✓	✓	5.970
22322	24028	\begin{align*} y^{\left (8\right )}+y&=x^{15} \\ \end{align*}	✓	✓	✓	✗	5.972
22323	24214	\begin{align*} \left (1+x^{2}-y^{2}\right ) y-x \left (-y^{2}+x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.972
22324	5098	\begin{align*} \left (2 x +3 y+2\right ) y^{\prime }&=1-2 x -3 y \\ \end{align*}	✓	✓	✓	✓	5.974
22325	6996	\begin{align*} -y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.975
22326	1231	\begin{align*} x +y+\left (x +2 y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.979
22327	5685	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	5.980
22328	19919	\begin{align*} x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.983
22329	9196	\begin{align*} y^{\prime }&=\frac {y^{2}+x^{2}}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✗	5.984
22330	21351	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	5.988
22331	20824	\begin{align*} x^{2}+y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.992
22332	13955	\begin{align*} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.994
22333	4837	\begin{align*} \left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\ \end{align*}	✓	✓	✓	✓	5.997
22334	4905	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (x^{2}+1\right )-y x \\ \end{align*}	✓	✓	✓	✓	5.998
22335	14228	\begin{align*} x^{\prime }&=t^{2} {\mathrm e}^{-x} \\ x \left (0\right ) &= \ln \left (2\right ) \\ \end{align*}	✓	✓	✓	✓	6.002
22336	2913	\begin{align*} x +y+\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.004
22337	19953	\begin{align*} y^{\prime }&=x^{3} y^{3}-y x \\ \end{align*}	✓	✓	✓	✓	6.005
22338	17065	\begin{align*} y^{\prime }&=-\frac {t}{y} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	6.007
22339	8684	\begin{align*} \left (x +2 y\right ) y^{\prime }&=1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	6.010
22340	25713	\begin{align*} \left (y^{2}+x^{2}\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	6.010
22341	4881	\begin{align*} x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	6.015
22342	2532	\begin{align*} y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\ y \left (0\right ) &= 100 \\ \end{align*}	✓	✓	✓	✓	6.016
22343	15965	\begin{align*} y^{\prime }&=\left (y-2\right ) \left (y+1-\cos \left (t \right )\right ) \\ \end{align*}	✓	✓	✓	✓	6.017
22344	6808	\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	6.018
22345	3461	\begin{align*} \left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	6.024
22346	8403	\begin{align*} y^{\prime }&=x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	6.026
22347	4802	\begin{align*} y^{\prime } x +2 y&=a \,x^{2 k} y^{k} \\ \end{align*}	✓	✓	✓	✓	6.027
22348	10279	\begin{align*} c y^{\prime }&=\frac {a x +b y^{2}}{r x} \\ \end{align*}	✓	✓	✓	✗	6.035
22349	13623	\begin{align*} x \left (2 a y+b x \right ) y^{\prime }&=a \left (2-m \right ) y^{2}+b \left (1-m \right ) x y+c \,x^{2}+A \,x^{m +2} \\ \end{align*}	✓	✓	✓	✗	6.036
22350	17271	\begin{align*} t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.036
22351	24205	\begin{align*} \frac {1}{\left (-y x +1\right )^{2}}+\left (y^{2}+\frac {x^{2}}{\left (-y x +1\right )^{2}}\right ) y^{\prime }&=0 \\ y \left (4\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	6.041
22352	5099	\begin{align*} \left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.042
22353	4211	\begin{align*} \sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y&=\sqrt {x +a}-\sqrt {x +b} \\ \end{align*}	✓	✓	✓	✗	6.043
22354	15895	\begin{align*} y^{\prime }&=\cos \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✗	6.044
22355	10017	\begin{align*} 2 t +3 x+\left (2+x\right ) x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.046
22356	16292	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	6.046
22357	24125	\begin{align*} y^{\prime }&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	6.047
22358	2945	\begin{align*} 2 y x +\left (y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.049
22359	2999	\begin{align*} y^{\prime }&=x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.049
22360	18340	\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y&=4 \,{\mathrm e}^{x} \\ y \left (-\infty \right ) &= 0 \\ y^{\prime }\left (-1\right ) &= -{\mathrm e}^{-1} \\ \end{align*}	✗	✓	✗	✗	6.050
22361	9205	\begin{align*} y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\ \end{align*}	✓	✓	✓	✗	6.052
22362	19091	\begin{align*} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }&=\left (1+y^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	6.054
22363	14043	\begin{align*} \left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	6.059
22364	17261	\begin{align*} \cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.062
22365	9736	\begin{align*} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✗	6.063
22366	19228	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	6.066
22367	11448	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.069
22368	8713	\begin{align*} y^{\prime } x&=y \ln \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	6.070
22369	2899	\begin{align*} x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.072
22370	17921	\begin{align*} x +y+\left (x -y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.073
22371	21407	\begin{align*} y^{\prime }+\left (b x +a \right ) y&=f \left (x \right ) \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	6.074
22372	5162	\begin{align*} 2 x y^{\prime } y&=4 x^{2} \left (2 x +1\right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	6.075
22373	17320	\begin{align*} y-t +\left (t +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.075
22374	5100	\begin{align*} \left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \\ \end{align*}	✓	✓	✓	✓	6.083
22375	17838	\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	6.083
22376	4890	\begin{align*} x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\ \end{align*}	✓	✓	✓	✓	6.095
22377	16962	\begin{align*} 2 x -y-y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	6.095
22378	12383	\begin{align*} y^{\prime \prime } x -\left (a +b \right ) \left (x +1\right ) y^{\prime }+a b x y&=0 \\ \end{align*}	✗	✓	✓	✗	6.098
22379	16859	\begin{align*} {\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.101
22380	20294	\begin{align*} y^{2}+2 x^{2} y+\left (2 x^{3}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.102
22381	3456	\begin{align*} y^{\prime }-x y^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	6.106
22382	12038	\begin{align*} y^{\prime }&=\frac {2 x^{3} y+x^{6}+y^{2} x^{2}+y^{3}}{x^{4}} \\ \end{align*}	✓	✓	✓	✗	6.108
22383	11742	\begin{align*} a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2}&=0 \\ \end{align*}	✓	✓	✗	✓	6.111
22384	19805	\begin{align*} y \left (3+y\right ) y^{\prime }&=x \left (3+2 y\right ) \\ \end{align*}	✓	✓	✓	✓	6.112
22385	3040	\begin{align*} y x -y^{2}-x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.113
22386	19955	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	6.113
22387	24189	\begin{align*} \cos \left (2 y\right )-3 y^{2} x^{2}+\left (\cos \left (2 y\right )-2 x \sin \left (2 y\right )-2 x^{3} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.118
22388	25769	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}	✗	✓	✓	✗	6.118
22389	24280	\begin{align*} y^{\prime } x&=y \left (2 y x +1\right ) \\ \end{align*}	✓	✓	✓	✓	6.119
22390	10130	\begin{align*} y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	6.122
22391	21511	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	6.129
22392	17885	\begin{align*} {\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.132
22393	3654	\begin{align*} y^{\prime }&=\frac {x +a y}{a x -y} \\ \end{align*}	✓	✓	✓	✗	6.136
22394	14028	\begin{align*} x y^{2} \left (y^{\prime } x +3 y\right )-2 y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	6.145
22395	17256	\begin{align*} 3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	6.145
22396	13234	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1} \\ \end{align*}	✓	✗	✓	✗	6.153
22397	2943	\begin{align*} y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.156
22398	6387	\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=a \,x^{2 k} {y^{\prime }}^{k} \\ \end{align*}	✓	✓	✓	✗	6.157
22399	23871	\begin{align*} y^{\prime }&=\frac {2 y x +3 y}{x^{2}+2 y^{2}} \\ \end{align*}	✗	✗	✗	✗	6.158
22400	8232	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	6.160