2.3.227 Problems 22601 to 22700

Table 2.1027: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22601	18506	\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	7.580
22602	11705	\begin{align*} {y^{\prime }}^{2} x +\left (y-3 x \right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	7.584
22603	22027	\begin{align*} 2 y x +x +\left (x^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.584
22604	13359	\begin{align*} y^{\prime }&=a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n} \\ \end{align*}	✓	✓	✓	✗	7.586
22605	13457	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y-a^{2} f \left (x \right )-a g \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	7.588
22606	9801	\begin{align*} 3 y y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	7.589
22607	21083	\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.589
22608	1592	\begin{align*} y^{\prime }&=2 x y \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.596
22609	15588	\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.596
22610	17006	\begin{align*} y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	7.597
22611	21255	\begin{align*} x^{\prime \prime }&=x^{3}-x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✗	7.604
22612	5670	\begin{align*} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	7.605
22613	12058	\begin{align*} y^{\prime }&=\frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \\ \end{align*}	✓	✓	✓	✗	7.605
22614	20870	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y&=5 x^{2} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.605
22615	15346	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.607
22616	24211	\begin{align*} y \left (x^{4}-y^{2}\right )+x \left (x^{4}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.610
22617	5004	\begin{align*} x^{n} y^{\prime }&=a +b \,x^{n -1} y \\ \end{align*}	✓	✓	✓	✗	7.616
22618	26409	\begin{align*} x^{2} y^{n} y^{\prime }&=2 x y^{\prime }-y \\ \end{align*}	✓	✓	✓	✗	7.619
22619	11918	\begin{align*} y^{\prime }&=\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \\ \end{align*}	✓	✓	✓	✗	7.620
22620	27454	\begin{align*} x y^{\prime }&=2 \sqrt {y}\, \cos \left (x \right )-2 y \\ \end{align*}	✓	✓	✓	✓	7.623
22621	2970	\begin{align*} \cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.624
22622	5021	\begin{align*} y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \\ \end{align*}	✓	✓	✓	✓	7.624
22623	4995	\begin{align*} \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	7.629
22624	25843	\begin{align*} y x -x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.633
22625	4731	\begin{align*} y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\ \end{align*}	✗	✗	✓	✓	7.634
22626	7751	\begin{align*} x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.634
22627	8319	\begin{align*} y^{\prime }&=1-\frac {y}{x} \\ y \left (-\frac {1}{2}\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	7.636
22628	12061	\begin{align*} y^{\prime }&=\frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \\ \end{align*}	✓	✓	✓	✓	7.638
22629	11607	\begin{align*} \left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	7.639
22630	13638	\begin{align*} y^{\prime }&=-y^{3}+3 a^{2} x^{2} y-2 a^{3} x^{3}+a \\ \end{align*}	✗	✓	✓	✗	7.639
22631	6144	\begin{align*} 8 y+\left (1-2 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.641
22632	9759	\begin{align*} 2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\ \end{align*}	✓	✓	✓	✗	7.642
22633	18509	\begin{align*} y^{\prime }&=\frac {b +a y}{d +c y} \\ \end{align*}	✓	✓	✓	✓	7.643
22634	8267	\begin{align*} x y^{\prime }+y&=2 x \\ y \left (x_{0} \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.647
22635	17878	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.650
22636	27437	\begin{align*} x y^{2}-x +\left (y x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.655
22637	22951	\begin{align*} x^{\prime }&=\frac {x}{t} \\ \end{align*}	✓	✓	✓	✓	7.656
22638	12884	\begin{align*} y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	7.658
22639	13216	\begin{align*} y^{\prime }&=\left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c \\ \end{align*}	✓	✓	✓	✗	7.660
22640	118	\begin{align*} y y^{\prime }+x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	7.661
22641	11914	\begin{align*} y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\ \end{align*}	✓	✓	✓	✓	7.661
22642	25470	\begin{align*} m y^{\prime \prime }+k y&=F \\ \end{align*}	✓	✓	✓	✓	7.661
22643	22991	\begin{align*} n^{\prime }&=k n-b t \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	7.663
22644	26294	\begin{align*} 2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \left (x \cos \left (x \right )-\sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	7.665
22645	22371	\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}	✓	✓	✓	✓	7.667
22646	22441	\begin{align*} y^{\prime }&=\frac {x +y}{x} \\ y \left (3\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	7.667
22647	8379	\begin{align*} x y^{\prime }&=y^{2}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	7.670
22648	2973	\begin{align*} \sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right )&=\cos \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	7.671
22649	25652	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	7.674
22650	17938	\begin{align*} \left (2 x -y^{2}\right ) y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	7.676
22651	12355	\begin{align*} a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	7.679
22652	11509	\begin{align*} y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}}&=0 \\ \end{align*}	✓	✓	✓	✓	7.683
22653	17109	\begin{align*} 1&=\cos \left (y\right ) y^{\prime } \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	7.683
22654	21989	\begin{align*} y^{\prime }&=-\frac {2 y}{x} \\ \end{align*}	✓	✓	✓	✓	7.689
22655	9930	\begin{align*} x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	7.691
22656	11878	\begin{align*} y^{\prime }&=\frac {F \left (\frac {1+x y^{2}}{x}\right )}{y x^{2}} \\ \end{align*}	✓	✓	✓	✗	7.691
22657	4672	\begin{align*} y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	7.692
22658	13453	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}+a n \,x^{n -1}-a^{2} x^{2 n} f \left (x \right ) \\ \end{align*}	✓	✗	✗	✗	7.693
22659	12221	\begin{align*} y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\ \end{align*}	✓	✓	✓	✗	7.698
22660	20828	\begin{align*} y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	7.706
22661	22497	\begin{align*} 1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.707
22662	22611	\begin{align*} y^{\prime }+y^{2}&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✗	7.707
22663	15565	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+4}+\sqrt {x} \\ y \left (3\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	7.708
22664	18046	\begin{align*} y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.708
22665	23213	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	7.709
22666	26268	\begin{align*} 2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.709
22667	12697	\begin{align*} y^{\prime \prime }&=-\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	7.711
22668	5416	\begin{align*} {y^{\prime }}^{2}+\left (1+2 y\right ) y^{\prime }+y \left (-1+y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	7.719
22669	21413	\begin{align*} y^{\prime }+\frac {y \left (x +y\right )}{x +2 y-1}&=0 \\ \end{align*}	✓	✓	✓	✓	7.731
22670	13336	\begin{align*} y^{\prime }&=y^{2}+\lambda a -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	7.733
22671	8303	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (3\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	7.734
22672	13346	\begin{align*} y^{\prime }&=a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n} \\ \end{align*}	✓	✗	✗	✗	7.734
22673	17840	\begin{align*} y^{\prime }&=\sqrt {x -y} \\ \end{align*}	✓	✓	✓	✓	7.735
22674	12766	\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 x y^{\prime }-y-2 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	7.737
22675	15382	\begin{align*} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.737
22676	21419	\begin{align*} 4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.737
22677	24366	\begin{align*} 2 y \left (x^{2}-y+x \right )+\left (x^{2}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	7.737
22678	18479	\begin{align*} y y^{\prime }&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	7.743
22679	3056	\begin{align*} 2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.747
22680	5127	\begin{align*} x y y^{\prime }&=a \,x^{3} \cos \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	7.753
22681	22295	\begin{align*} 2 x +y+\left (x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.756
22682	14770	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	7.758
22683	17940	\begin{align*} y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\ \end{align*}	✓	✓	✓	✓	7.760
22684	11926	\begin{align*} y^{\prime }&=\frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3} \\ \end{align*}	✓	✓	✓	✗	7.761
22685	18102	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	7.763
22686	25871	\begin{align*} y y^{\prime }+y^{2} \cot \left (x \right )&=\csc \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	7.763
22687	15393	\begin{align*} y&=x y^{\prime }+\sqrt {1-{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	7.768
22688	14234	\begin{align*} y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	7.769
22689	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*}	✓	✓	✓	✗	7.774
22690	2992	\begin{align*} r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\ \end{align*}	✓	✓	✓	✓	7.775
22691	4329	\begin{align*} x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	7.776
22692	13340	\begin{align*} y^{\prime }&=y^{2}+\lambda a -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\ \end{align*}	✗	✓	✓	✗	7.776
22693	8690	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.779
22694	12215	\begin{align*} y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 x^{2} y^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\ \end{align*}	✓	✓	✓	✓	7.779
22695	21058	\begin{align*} x^{\prime }&=-\frac {t}{4 x^{3}} \\ x \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	7.780
22696	17980	\begin{align*} 1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	7.783
22697	21063	\begin{align*} x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\ \end{align*}	✓	✓	✓	✓	7.784
22698	22599	\begin{align*} y^{\prime }&={\mathrm e}^{x +3 y}+1 \\ \end{align*}	✓	✓	✓	✓	7.787
22699	12696	\begin{align*} y^{\prime \prime }&=-\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \\ \end{align*}	✗	✓	✓	✗	7.789
22700	12219	\begin{align*} y^{\prime }&=\frac {-32 y x +16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 x^{2} y^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \\ \end{align*}	✓	✓	✓	✓	7.792