2.3.210 Problems 20901 to 21000

Table 2.951: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20901	6980	\begin{align*} y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.882
20902	1558	\begin{align*} \left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y&=\left (x -2\right )^{3} \\ \end{align*}	✓	✓	✓	✓	3.883
20903	4277	\begin{align*} y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	3.885
20904	5080	\begin{align*} \left (x -2 y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.885
20905	7003	\begin{align*} y^{\prime } x +y&=x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.885
20906	25029	\begin{align*} y-t +\left (t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.887
20907	12688	\begin{align*} y^{\prime \prime }&=-\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	3.889
20908	19359	\begin{align*} y^{\prime \prime } x&=y^{\prime }+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✓	3.890
20909	4991	\begin{align*} x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y&=y^{2} \\ \end{align*}	✓	✓	✓	✗	3.891
20910	5281	\begin{align*} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.891
20911	117	\begin{align*} y^{\prime } x&=y+\sqrt {y^{2}+x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.892
20912	6897	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.892
20913	16294	\begin{align*} y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.894
20914	17060	\begin{align*} y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\ y \left (3\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.895
20915	12391	\begin{align*} y^{\prime \prime } x +\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	3.898
20916	4266	\begin{align*} \left (x +y\right ) y^{\prime }&=y-x \\ \end{align*}	✓	✓	✓	✓	3.899
20917	14454	\begin{align*} 4 x +3 y^{2}+2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	3.900
20918	20760	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \\ \end{align*}	✓	✓	✓	✓	3.900
20919	2940	\begin{align*} x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.901
20920	13698	\begin{align*} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.901
20921	4952	\begin{align*} 2 x^{2} y^{\prime }+1+2 y x -y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.902
20922	4869	\begin{align*} x^{2} y^{\prime }&=\left (b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	3.904
20923	5833	\begin{align*} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.904
20924	13237	\begin{align*} y^{\prime } x&=a y^{2}+b y+c \,x^{2 b} \\ \end{align*}	✓	✓	✓	✗	3.905
20925	53	\begin{align*} y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.907
20926	25047	\begin{align*} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.907
20927	12301	\begin{align*} y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.908
20928	4632	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \sec \left (x \right )^{2}-2 y \cot \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	3.909
20929	6869	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-\frac {2 a}{3}} \\ \end{align*}	✓	✓	✓	✗	3.910
20930	23971	\begin{align*} y^{\prime }-y x&=x \\ \end{align*}	✓	✓	✓	✓	3.910
20931	14245	\begin{align*} 7 t^{2} x^{\prime }&=3 x-2 t \\ \end{align*}	✓	✓	✓	✓	3.911
20932	4628	\begin{align*} y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	3.914
20933	6431	\begin{align*} y y^{\prime \prime }&=\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.914
20934	7908	\begin{align*} 1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.914
20935	4274	\begin{align*} \left (-y x +1\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.915
20936	14163	\begin{align*} 2 y^{\prime \prime }&={\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.915
20937	21008	\begin{align*} x^{\prime }-2 x \cos \left (t \right )&=\cos \left (t \right ) \\ x \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	3.915
20938	20688	\begin{align*} \left (x +2 y^{3}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	3.916
20939	3638	\begin{align*} \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	3.918
20940	13692	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.918
20941	4210	\begin{align*} \sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \\ \end{align*}	✓	✓	✓	✗	3.919
20942	15926	\begin{align*} y^{\prime }-\frac {3 y}{t}&=2 t^{3} {\mathrm e}^{2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.924
20943	17879	\begin{align*} 1+y^{2}&=y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	3.924
20944	21411	\begin{align*} y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.924
20945	23173	\begin{align*} \left (1-x \right ) y^{\prime }+y x&=x \left (x -1\right )^{2} \\ y \left (5\right ) &= 24 \\ \end{align*}	✓	✓	✓	✓	3.924
20946	1725	\begin{align*} \sin \left (y\right ) y+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.925
20947	14242	\begin{align*} x^{\prime }&=2 t^{3} x-6 \\ \end{align*}	✓	✓	✓	✓	3.925
20948	5182	\begin{align*} x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.927
20949	4825	\begin{align*} y^{\prime } x&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✗	3.928
20950	8347	\begin{align*} y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.928
20951	14548	\begin{align*} 5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.928
20952	19795	\begin{align*} y^{\prime }+y \cos \left (x \right )&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	3.928
20953	20632	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-y \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.929
20954	19255	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.931
20955	4799	\begin{align*} y^{\prime } x +y&=a \left (-x^{2}+1\right ) y^{3} \\ \end{align*}	✓	✓	✓	✓	3.933
20956	5011	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.935
20957	11637	\begin{align*} \left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.937
20958	15046	\begin{align*} x^{\prime }&=\frac {x}{t}+\frac {x^{2}}{t^{3}} \\ x \left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	3.937
20959	17932	\begin{align*} y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.937
20960	20233	\begin{align*} \frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.937
20961	7559	\begin{align*} 2 \cos \left (2 x +y\right )-x^{2}+\left (\cos \left (2 x +y\right )+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.938
20962	11756	\begin{align*} y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	3.939
20963	7507	\begin{align*} y^{\prime }&=\left (x -y+5\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.945
20964	23941	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.945
20965	11867	\begin{align*} y^{\prime }&=\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \\ \end{align*}	✓	✓	✓	✗	3.946
20966	23125	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.946
20967	8404	\begin{align*} y^{\prime }&=\sqrt {1+y^{2}}\, \sin \left (y\right )^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	3.947
20968	21325	\begin{align*} -x^{\prime \prime }+x&={\mathrm e}^{-x} \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	3.947
20969	20019	\begin{align*} \sqrt {x}\, y^{\prime }&=\sqrt {y} \\ \end{align*}	✓	✓	✓	✓	3.949
20970	9080	\begin{align*} y^{\prime }&=\frac {2 x y^{2}}{1-x^{2} y} \\ \end{align*}	✓	✓	✓	✓	3.951
20971	5850	\begin{align*} \left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	3.953
20972	17333	\begin{align*} -y+y^{\prime }&=t y^{3} \\ \end{align*}	✓	✓	✓	✓	3.954
20973	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*}	✓	✓	✓	✓	3.954
20974	21356	\begin{align*} y^{\prime }&=x^{2} y \\ \end{align*}	✓	✓	✓	✓	3.956
20975	25016	\begin{align*} \frac {y}{t}+y^{\prime }&=y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.956
20976	15566	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	3.957
20977	24148	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.960
20978	19493	\begin{align*} y^{\prime \prime }+3 y^{\prime } x +x^{2} y&=0 \\ \end{align*}	✗	✓	✓	✗	3.961
20979	13718	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a \left (n +1\right ) x^{n -1}+b \left (m +1\right ) x^{m -1}\right ) y&=0 \\ \end{align*}	✓	✓	✗	✗	3.962
20980	23210	\begin{align*} y x -\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.964
20981	19148	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	3.965
20982	110	\begin{align*} \left (x +2 y\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.967
20983	779	\begin{align*} y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\ \end{align*}	✓	✓	✓	✓	3.967
20984	5334	\begin{align*} y^{\prime } \sqrt {b^{2}-y^{2}}&=\sqrt {a^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.967
20985	7400	\begin{align*} \frac {y^{\prime }}{\theta }&=\frac {y \sin \left (\theta \right )}{y^{2}+1} \\ y \left (\pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.968
20986	11617	\begin{align*} \left (a y^{3} x +c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.968
20987	24134	\begin{align*} \theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.969
20988	4868	\begin{align*} x^{2} y^{\prime }&=a +b x y \\ \end{align*}	✓	✓	✓	✓	3.970
20989	8303	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (3\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.970
20990	13205	\begin{align*} g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	3.970
20991	1585	\begin{align*} y^{\prime }&=\left (x -1\right ) \left (y-1\right ) \left (y-2\right ) \\ \end{align*}	✓	✓	✓	✓	3.971
20992	8231	\begin{align*} \left (y-x \right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	3.971
20993	24315	\begin{align*} y \left (y^{2} x^{2}+x^{2}+y^{2}\right )+x \left (x^{2}+y^{2}-y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.971
20994	2853	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.972
20995	8787	\begin{align*} y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\ \end{align*}	✓	✓	✓	✓	3.972
20996	4967	\begin{align*} x^{3} y^{\prime }&=b \,x^{2} y+a \\ \end{align*}	✓	✓	✓	✓	3.973
20997	1588	\begin{align*} y^{\prime }+x \left (y^{2}+y\right )&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.974
20998	1645	\begin{align*} y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	3.974
20999	17964	\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x +1 \\ \end{align*}	✓	✓	✓	✓	3.975
21000	4803	\begin{align*} y^{\prime } x&=4 y-4 \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	3.976