2.3.247 Problems 24601 to 24700

Table 2.1025: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24601	19067	\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	27.748
24602	7462	\begin{align*} 2 x +y^{2}-\cos \left (x +y\right )+\left (2 y x -\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	27.799
24603	19781	\begin{align*} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=r y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✗	27.838
24604	13635	\begin{align*} x \left (2 a \,x^{n} y+b \right ) y^{\prime }&=-a \left (3 n +m \right ) x^{n} y^{2}-b \left (2 n +m \right ) y+A \,x^{m}+x \,x^{-n} \\ \end{align*}	✓	✓	✓	✗	27.863
24605	201	\begin{align*} {\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	27.870
24606	19733	\begin{align*} \sqrt {t^{2}+T}&=T^{\prime } \\ \end{align*}	✓	✓	✓	✗	27.889
24607	5628	\begin{align*} {y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y}&=0 \\ \end{align*}	✓	✓	✗	✗	27.951
24608	5988	\begin{align*} \left (m +1\right ) x^{m} a \left (m \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✓	27.969
24609	17049	\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (-4\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	27.977
24610	19912	\begin{align*} \left (y x +1\right ) y-x \left (-y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	27.984
24611	19933	\begin{align*} y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	28.033
24612	19706	\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \\ \end{align*}	✓	✓	✓	✓	28.064
24613	13299	\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }&=y^{2}+k \,{\mathrm e}^{\nu x} y-m^{2}+k m \,{\mathrm e}^{\nu x} \\ \end{align*}	✓	✓	✓	✗	28.092
24614	22423	\begin{align*} y^{\prime }&=\frac {2 \sin \left (2 x \right )-\tan \left (y\right )}{x \sec \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✗	✓	✗	28.106
24615	15618	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	28.122
24616	22529	\begin{align*} \tan \left (y\right )-\tan \left (y\right )^{2} \cos \left (x \right )-x \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.130
24617	19923	\begin{align*} 2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.137
24618	24003	\begin{align*} y^{\prime \prime \prime }-y&=x^{n} \\ \end{align*}	✓	✓	✓	✓	28.137
24619	4778	\begin{align*} y^{\prime } x&=a \,x^{n}+b y+c y^{2} \\ \end{align*}	✓	✓	✓	✗	28.151
24620	10044	\begin{align*} y^{\prime }&=-4 \sin \left (x -y\right )-4 \\ \end{align*}	✓	✓	✓	✓	28.224
24621	15291	\begin{align*} x^{\prime }&=-3 x-3 y+z \\ y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	28.240
24622	19289	\begin{align*} 2 x -2 y+\left (y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.251
24623	15940	\begin{align*} y^{\prime }&=-\sin \left (y\right )^{5} \\ \end{align*}	✓	✓	✓	✓	28.319
24624	11531	\begin{align*} x y^{\prime } y-y^{2}+y x +x^{3}-2 x^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	28.378
24625	25025	\begin{align*} y^{\prime }&=\tan \left (y\right )+\frac {2 \cos \left (t \right )}{\cos \left (y\right )} \\ \end{align*}	✓	✓	✓	✗	28.393
24626	4789	\begin{align*} y^{\prime } x +a \,x^{2} y^{2}+2 y&=b \\ \end{align*}	✓	✓	✓	✗	28.418
24627	19121	\begin{align*} x&=y^{\prime } y+a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	28.454
24628	21930	\begin{align*} x y^{2}&=y-y^{\prime } x \\ \end{align*}	✓	✓	✓	✓	28.459
24629	23218	\begin{align*} y^{\prime }&=\frac {x -y+5}{2 x -y-3} \\ \end{align*}	✓	✓	✓	✗	28.541
24630	11906	\begin{align*} y^{\prime }&=\frac {x^{2}}{y+x^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✓	28.606
24631	5923	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	28.659
24632	4286	\begin{align*} y^{2} {\mathrm e}^{y x}+\cos \left (x \right )+\left ({\mathrm e}^{y x}+x y \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	28.667
24633	4084	\begin{align*} 3 x -y-6+\left (x +y+2\right ) y^{\prime }&=0 \\ y \left (2\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	28.736
24634	21860	\begin{align*} y^{2}-2 x y^{\prime } y+x^{2} {y^{\prime }}^{2}-{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	28.741
24635	12408	\begin{align*} 5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{{1}/{5}} y&=0 \\ \end{align*}	✗	✓	✓	✗	28.757
24636	19277	\begin{align*} x^{2} y^{\prime }&=3 \left (y^{2}+x^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\ \end{align*}	✓	✓	✓	✓	28.765
24637	3580	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \\ y \left (\pi \right ) &= \frac {1}{\pi } \\ \end{align*}	✓	✓	✓	✓	28.832
24638	5422	\begin{align*} {y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \\ \end{align*}	✓	✓	✓	✗	28.836
24639	2524	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	28.846
24640	5985	\begin{align*} -\left (c \,x^{2}+b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	28.851
24641	2934	\begin{align*} \frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	28.859
24642	17085	\begin{align*} 3 \sin \left (t \right )-\sin \left (3 t \right )&=\left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✗	28.892
24643	20011	\begin{align*} {y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \\ \end{align*}	✓	✓	✗	✗	28.906
24644	19770	\begin{align*} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✗	28.941
24645	15258	\begin{align*} t^{3} y^{\prime \prime }-2 t y^{\prime }+y&=t^{4} \\ \end{align*}	✗	✓	✓	✗	28.960
24646	13968	\begin{align*} \frac {1}{\sqrt {y^{2}+x^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {y^{2}+x^{2}}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	28.990
24647	20989	\begin{align*} y^{\prime }&=x^{3}+y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	28.991
24648	10436	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \\ \end{align*}	✓	✓	✓	✗	29.075
24649	11367	\begin{align*} y^{\prime }-\frac {\sqrt {{| y \left (y-1\right ) \left (-1+a y\right )|}}}{\sqrt {{| x \left (x -1\right ) \left (a x -1\right )|}}}&=0 \\ \end{align*}	✓	✓	✓	✓	29.106
24650	19238	\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\ \end{align*}	✓	✓	✓	✓	29.151
24651	15856	\begin{align*} y^{\prime }&=y^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	29.214
24652	20964	\begin{align*} y^{\prime }&=\frac {x +y+1}{2+x}-{\mathrm e}^{\frac {x +y+1}{2+x}} \\ \end{align*}	✓	✓	✓	✗	29.241
24653	12612	\begin{align*} y^{\prime \prime }&=-\frac {\left (x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \\ \end{align*}	✗	✓	✓	✗	29.338
24654	12108	\begin{align*} y^{\prime }&=\frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✗	29.341
24655	13568	\begin{align*} y^{\prime } y&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\ \end{align*}	✗	✗	✗	✗	29.354
24656	10405	\begin{align*} y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	29.458
24657	20433	\begin{align*} \left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\ \end{align*}	✗	✓	✓	✗	29.470
24658	13735	\begin{align*} y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	29.482
24659	5475	\begin{align*} x {y^{\prime }}^{2}-a y y^{\prime }+b&=0 \\ \end{align*}	✓	✓	✓	✗	29.484
24660	24167	\begin{align*} y^{2} y^{\prime }&=x \left (-y+y^{\prime } x \right ) {\mathrm e}^{\frac {x}{y}} \\ \end{align*}	✓	✓	✓	✓	29.495
24661	17254	\begin{align*} -y+t y^{\prime }&=t y^{3} \sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	29.561
24662	19916	\begin{align*} x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.619
24663	5336	\begin{align*} y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\ \end{align*}	✓	✓	✓	✗	29.647
24664	13551	\begin{align*} y^{\prime } y-y&=a x +b \,x^{m} \\ \end{align*}	✗	✗	✗	✗	29.658
24665	19144	\begin{align*} a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	29.674
24666	19935	\begin{align*} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	29.674
24667	20970	\begin{align*} y^{\prime }&=\frac {y \ln \left (y\right )}{\sin \left (x \right )} \\ y \left (\frac {\pi }{2}\right ) &= {\mathrm e}^{{\mathrm e}} \\ \end{align*}	✓	✓	✓	✓	29.682
24668	7492	\begin{align*} \left (t +x+2\right ) x^{\prime }+3 t -x-6&=0 \\ \end{align*}	✓	✓	✓	✓	29.697
24669	13732	\begin{align*} y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	29.734
24670	11814	\begin{align*} {y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x&=0 \\ \end{align*}	✓	✓	✓	✗	29.757
24671	21859	\begin{align*} 2 y a \,x^{3}-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	29.809
24672	4713	\begin{align*} y^{\prime }&=y \sqrt {a +b y} \\ \end{align*}	✓	✓	✓	✓	29.816
24673	20439	\begin{align*} y^{\prime } y+x&=a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	29.817
24674	2350	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	29.829
24675	5352	\begin{align*} \left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	29.905
24676	20681	\begin{align*} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.906
24677	24156	\begin{align*} 5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	29.949
24678	22992	\begin{align*} y^{\prime } x -2 y \cos \left (x \right )&={\mathrm e}^{x} \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✗	29.964
24679	17253	\begin{align*} 2 t y^{\prime }-y&=2 t y^{3} \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	30.071
24680	13036	\begin{align*} \left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	30.095
24681	25054	\begin{align*} y^{\prime }&=\cos \left (t +y\right ) \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}	✓	✗	✓	✓	30.097
24682	14155	\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y&=0 \\ \end{align*}	✗	✓	✗	✗	30.127
24683	10432	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✗	✓	✗	✗	30.182
24684	4331	\begin{align*} 3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	30.203
24685	7503	\begin{align*} y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\ \end{align*}	✓	✓	✓	✓	30.240
24686	2349	\begin{align*} y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	30.248
24687	5987	\begin{align*} -\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	30.299
24688	25506	\begin{align*} y^{\prime }&=-\frac {1+{\mathrm e}^{t y} y}{2 y+{\mathrm e}^{t y} t} \\ \end{align*}	✓	✓	✓	✗	30.301
24689	21385	\begin{align*} y^{2}-x^{2}-2 x y^{\prime } y&=0 \\ \end{align*}	✓	✓	✓	✓	30.306
24690	2514	\begin{align*} 2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	30.360
24691	11629	\begin{align*} \left (\sqrt {1+y^{2}}+a x \right ) y^{\prime }+\sqrt {x^{2}+1}+a y&=0 \\ \end{align*}	✓	✓	✓	✗	30.398
24692	1723	\begin{align*} \cos \left (x \right ) \cos \left (y\right )+\left (\cos \left (y\right ) \sin \left (x \right )-\sin \left (x \right ) \sin \left (y\right )+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	30.400
24693	2955	\begin{align*} y-x^{2} \sqrt {x^{2}-y^{2}}-y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	30.411
24694	3425	\begin{align*} y^{\prime }&=-y^{3} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	30.428
24695	17231	\begin{align*} 2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	30.435
24696	6994	\begin{align*} y^{\prime } \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	30.441
24697	12410	\begin{align*} 2 a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+c y&=0 \\ \end{align*}	✗	✓	✓	✗	30.457
24698	22602	\begin{align*} {y^{\prime }}^{2}+\left (3 y-2 x \right ) y^{\prime }-6 y&=0 \\ \end{align*}	✓	✓	✓	✗	30.517
24699	21872	\begin{align*} y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	30.557
24700	19954	\begin{align*} y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	30.568