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	5275	\begin{align*} x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	6.737
22302	22697	\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	6.740
22303	2536	\begin{align*} y^{\prime }&=t \sqrt {1-y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.741
22304	11783	\begin{align*} \left (-x +y\right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.744
22305	9520	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	6.746
22306	13358	\begin{align*} y^{\prime }&=a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	6.746
22307	22384	\begin{align*} y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✗	6.747
22308	23194	\begin{align*} y-x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.750
22309	16894	\begin{align*} \left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.751
22310	747	\begin{align*} x^{2} y^{\prime }+2 x y&=5 y^{3} \\ \end{align*}	✓	✓	✓	✓	6.765
22311	20466	\begin{align*} y^{2} \left (y-x y^{\prime }\right )&=x^{4} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	6.768
22312	23162	\begin{align*} y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	6.769
22313	23905	\begin{align*} y^{\prime }+3 y&=1+x \\ \end{align*}	✓	✓	✓	✓	6.770
22314	27437	\begin{align*} x y^{2}-x +\left (x y+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.771
22315	9530	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	6.773
22316	25757	\begin{align*} x y^{\prime }+y&=\frac {1}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	6.776
22317	4423	\begin{align*} y^{4}+x y+\left (x y^{3}-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.780
22318	19729	\begin{align*} y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	6.781
22319	17578	\begin{align*} 2 y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	6.782
22320	3021	\begin{align*} 2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.783
22321	23134	\begin{align*} x y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	6.792
22322	528	\begin{align*} y^{\prime }&=y^{2}+x^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	6.793
22323	5123	\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	6.795
22324	27234	\begin{align*} y^{2}-2 x y+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.797
22325	2935	\begin{align*} \frac {2 x^{2}}{y^{2}+x^{2}}+\ln \left (y^{2}+x^{2}\right )+\frac {2 x y y^{\prime }}{y^{2}+x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	6.798
22326	26153	\begin{align*} y^{\prime } y+x&=0 \\ \end{align*}	✓	✓	✓	✓	6.798
22327	27450	\begin{align*} y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\ \end{align*}	✓	✓	✓	✓	6.801
22328	14907	\begin{align*} 2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.802
22329	24198	\begin{align*} 2 x +y \cos \left (x y\right )+x \cos \left (x y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.802
22330	24569	\begin{align*} 4 y^{\prime \prime }+y&=2 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.802
22331	8671	\begin{align*} \frac {y}{-1+x}+\frac {x y^{\prime }}{1+y}&=0 \\ \end{align*}	✓	✓	✓	✓	6.803
22332	8310	\begin{align*} y^{\prime } y&=-x \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	6.806
22333	20029	\begin{align*} y&=x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	6.808
22334	3246	\begin{align*} y^{3} y^{\prime \prime }+4&=0 \\ \end{align*}	✓	✓	✓	✗	6.809
22335	16304	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\ \end{align*}	✓	✓	✓	✓	6.812
22336	16219	\begin{align*} y^{\prime }&=y^{2}+9 \\ \end{align*}	✓	✓	✓	✓	6.813
22337	9010	\begin{align*} y^{\prime }&=x^{2} y^{2}-4 x^{2} \\ \end{align*}	✓	✓	✓	✗	6.816
22338	24134	\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	6.816
22339	14269	\begin{align*} x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\ \end{align*}	✓	✓	✓	✓	6.825
22340	22629	\begin{align*} 4 y^{\prime \prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	6.825
22341	7876	\begin{align*} x y y^{\prime }+x^{2}+y^{2}&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	6.828
22342	11652	\begin{align*} 3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y&=0 \\ \end{align*}	✓	✓	✓	✓	6.828
22343	21859	\begin{align*} 2 a \,x^{3} y-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	6.828
22344	3603	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.829
22345	16349	\begin{align*} y^{\prime }&=\frac {3 y}{1+x}-y^{2} \\ \end{align*}	✓	✓	✓	✓	6.836
22346	7254	\begin{align*} y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	6.838
22347	17932	\begin{align*} y^{\prime }-2 x y&=2 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	6.838
22348	16279	\begin{align*} x y^{\prime }+3 y&=20 x^{2} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	6.839
22349	9192	\begin{align*} x y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	6.847
22350	21398	\begin{align*} y^{\prime }&=\frac {y^{2}+x^{2}}{x y} \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	6.847
22351	3286	\begin{align*} 1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	6.848
22352	16374	\begin{align*} y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.848
22353	3679	\begin{align*} y^{\prime }+\frac {7 y}{x}-3 y^{2}&=\frac {3}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	6.852
22354	8244	\begin{align*} y^{\prime } y&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	6.853
22355	21622	\begin{align*} y^{\prime }&=\alpha \left (A -y\right ) y \\ \end{align*}	✓	✓	✓	✓	6.854
22356	13028	\begin{align*} \left (-y+x y^{\prime }\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2}&=0 \\ \end{align*}	✗	✓	✗	✗	6.855
22357	17237	\begin{align*} -4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	6.862
22358	779	\begin{align*} x y^{\prime }+2 y&=6 x^{2} \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	6.863
22359	6037	\begin{align*} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	6.863
22360	17296	\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\ \end{align*}	✓	✓	✓	✓	6.863
22361	19738	\begin{align*} y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \\ \end{align*}	✓	✓	✓	✗	6.865
22362	20776	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	6.865
22363	3315	\begin{align*} x&=y^{\prime } y+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	6.866
22364	12404	\begin{align*} 4 x y^{\prime \prime }+4 m y^{\prime }-\left (x -2 m -4 n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	6.867
22365	16358	\begin{align*} 1-\left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.869
22366	11960	\begin{align*} y^{\prime }&=\frac {y+x^{3} a \ln \left (1+x \right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (1+x \right )-x^{2} y^{2}-x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	6.874
22367	3626	\begin{align*} x^{\prime }+\frac {2 x}{-t +4}&=5 \\ x \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	6.878
22368	19093	\begin{align*} y^{\prime }&=\frac {x -y^{2}}{2 y \left (x +y^{2}\right )} \\ \end{align*}	✓	✓	✓	✓	6.878
22369	11985	\begin{align*} y^{\prime }&=\frac {-y \,{\mathrm e}^{x}+x y-x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (x -{\mathrm e}^{x}\right ) x} \\ \end{align*}	✓	✓	✓	✗	6.880
22370	14417	\begin{align*} x^{2}+y^{2}+2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.880
22371	3451	\begin{align*} t y^{\prime }&=-y+t^{3} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	6.883
22372	11962	\begin{align*} y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 x^{2} y^{2}+7 x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	6.884
22373	6021	\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	6.891
22374	12268	\begin{align*} y^{\prime }&=-F \left (x \right ) \left (y^{2}-2 x y-x^{2}\right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	6.892
22375	19375	\begin{align*} x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	6.894
22376	23940	\begin{align*} y^{\prime }&=f \left (x \right )+a y+b z \\ z^{\prime }&=g \left (x \right )+c y+d z \\ \end{align*}	✓	✓	✓	✓	6.894
22377	11968	\begin{align*} y^{\prime }&=\frac {y+\ln \left (\left (-1+x \right ) \left (1+x \right )\right ) x^{3}+7 \ln \left (\left (-1+x \right ) \left (1+x \right )\right ) x y^{2}}{x} \\ \end{align*}	✓	✓	✓	✗	6.895
22378	22993	\begin{align*} \sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3} \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.902
22379	15648	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	6.906
22380	14519	\begin{align*} \left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	6.911
22381	8825	\begin{align*} \phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\ \end{align*}	✓	✓	✓	✓	6.917
22382	19413	\begin{align*} x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	6.919
22383	12680	\begin{align*} y^{\prime \prime }&=-\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}-y \sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	6.921
22384	23151	\begin{align*} x y^{\prime }+y&=3 \\ \end{align*}	✓	✓	✓	✓	6.931
22385	23384	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	6.935
22386	16200	\begin{align*} x^{2} y^{\prime }+x y^{2}&=x \\ \end{align*}	✓	✓	✓	✓	6.936
22387	26227	\begin{align*} x y^{2} \left (x y^{\prime }+y\right )&=a^{2} \\ \end{align*}	✓	✓	✓	✓	6.937
22388	26912	\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	6.938
22389	4352	\begin{align*} 2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	6.941
22390	11654	\begin{align*} \left (x \sin \left (x y\right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (x y\right )+\cos \left (x +y\right )+\cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	6.941
22391	3257	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	6.944
22392	24799	\begin{align*} 4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	6.947
22393	9492	\begin{align*} y^{\prime }&=y+x \,{\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	6.951
22394	3317	\begin{align*} y&=y^{\prime } x \left (y^{\prime }+1\right ) \\ \end{align*}	✓	✓	✓	✓	6.953
22395	20716	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\ \end{align*}	✓	✓	✓	✓	6.954
22396	17905	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\ y \left (-\infty \right ) &= \frac {7 \pi }{2} \\ \end{align*}	✓	✓	✗	✗	6.956
22397	7490	\begin{align*} \left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	6.957
22398	7464	\begin{align*} \frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (x y\right )+\left (x \cos \left (x y\right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	6.961
22399	27226	\begin{align*} \left (x +2 y\right ) y^{\prime }&=1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	6.963
22400	5455	\begin{align*} {y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	6.980