2.3.257 Problems 25601 to 25700

Table 2.1087: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
25601	27052	\begin{align*} t^{2} y^{\prime }-2 y&=2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	24.920
25602	11516	\begin{align*} \left (y-x^{2}\right ) y^{\prime }+4 y x&=0 \\ \end{align*}	✓	✓	✓	✓	24.921
25603	17843	\begin{align*} y^{\prime }&=\frac {y+1}{x -y} \\ \end{align*}	✓	✓	✓	✓	24.931
25604	24349	\begin{align*} 2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	24.936
25605	27481	\begin{align*} y&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	24.944
25606	6145	\begin{align*} a y-\left (1-2 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	24.987
25607	17288	\begin{align*} t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	25.006
25608	13804	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+x^{n -1} a c +b^{2} x^{2}+2 b c x +c^{2}-c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	25.010
25609	22570	\begin{align*} y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	25.041
25610	15869	\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	25.070
25611	5083	\begin{align*} \left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\ \end{align*}	✓	✓	✓	✓	25.073
25612	11748	\begin{align*} \left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\ \end{align*}	✗	✗	✗	✗	25.104
25613	5087	\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\ \end{align*}	✓	✓	✓	✓	25.133
25614	16241	\begin{align*} \left (y^{2}-1\right ) y^{\prime }&=4 x y^{2} \\ \end{align*}	✓	✓	✓	✓	25.142
25615	5104	\begin{align*} \left (5+3 x -4 y\right ) y^{\prime }&=2+7 x -3 y \\ \end{align*}	✓	✓	✓	✓	25.143
25616	5221	\begin{align*} \left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✗	25.152
25617	15453	\begin{align*} x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \\ \end{align*}	✓	✓	✓	✓	25.157
25618	14271	\begin{align*} x^{\prime }&=a x+b x^{3} \\ \end{align*}	✓	✓	✓	✓	25.169
25619	19402	\begin{align*} \frac {-x +y}{\left (x +y\right )^{3}}-\frac {2 x y^{\prime }}{\left (x +y\right )^{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	25.189
25620	5581	\begin{align*} \left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	25.211
25621	24367	\begin{align*} y \left (1+2 x -y\right )+x \left (3 x -4 y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	25.233
25622	9128	\begin{align*} 2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	25.234
25623	14450	\begin{align*} 2 \sin \left (x \right ) \cos \left (x \right ) y+\sin \left (x \right ) y^{2}+\left (\sin \left (x \right )^{2}-2 \cos \left (x \right ) y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	25.238
25624	1677	\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 x^{2} y^{2}+6 y x +2}{x^{2} \left (2 y x +3\right )} \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	25.243
25625	14535	\begin{align*} 3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	25.248
25626	26999	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	25.270
25627	24398	\begin{align*} \left (x -1\right ) y-\left (x^{2}-2 x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.277
25628	14469	\begin{align*} x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	25.282
25629	23292	\begin{align*} y y^{\prime }+y^{\prime \prime }&=2 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	25.283
25630	25025	\begin{align*} y^{\prime }&=\tan \left (y\right )+\frac {2 \cos \left (t \right )}{\cos \left (y\right )} \\ \end{align*}	✓	✓	✓	✗	25.289
25631	25875	\begin{align*} x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	25.310
25632	2517	\begin{align*} 3 y t +y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	25.312
25633	21839	\begin{align*} y^{3} \left (y y^{\prime }+x \right )&=\left (x^{2}+y^{2}\right )^{3} y^{\prime } \\ \end{align*}	✓	✗	✗	✗	25.320
25634	18614	\begin{align*} y^{\prime }&=a y+b y^{3} \\ \end{align*}	✓	✓	✓	✓	25.325
25635	27000	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=0 \\ \end{align*}	✓	✓	✓	✓	25.358
25636	11832	\begin{align*} {y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (-1+2 y\right ) y^{\prime }+3 x&=0 \\ \end{align*}	✓	✓	✓	✗	25.403
25637	25732	\begin{align*} y^{\prime }&=x \sqrt {y} \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	25.421
25638	21428	\begin{align*} y^{\prime }&=\frac {x -2 y}{2 x -y} \\ \end{align*}	✓	✓	✓	✓	25.436
25639	2929	\begin{align*} \cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.441
25640	26998	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	25.447
25641	7408	\begin{align*} y^{\prime }&=\sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	25.469
25642	27003	\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+58 y&=0 \\ \end{align*}	✓	✓	✓	✓	25.498
25643	8159	\begin{align*} \sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \\ \end{align*}	✗	✗	✗	✗	25.509
25644	13372	\begin{align*} y^{\prime }&=\left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	25.522
25645	17929	\begin{align*} x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.529
25646	13420	\begin{align*} y^{\prime }&=y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\arcsin \left (x \right )^{n} \lambda \\ \end{align*}	✓	✓	✓	✗	25.560
25647	24232	\begin{align*} 2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	25.582
25648	5546	\begin{align*} y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	25.589
25649	9456	\begin{align*} i^{\prime \prime }+2 i^{\prime }+3 i&=\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \\ i \left (0\right ) &= 8 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✗	25.589
25650	2985	\begin{align*} x y y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✓	25.618
25651	12569	\begin{align*} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	25.624
25652	4275	\begin{align*} 2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.625
25653	5162	\begin{align*} 2 x y y^{\prime }&=4 x^{2} \left (2 x +1\right )+y^{2} \\ \end{align*}	✓	✓	✓	✓	25.647
25654	17261	\begin{align*} \cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	25.664
25655	22983	\begin{align*} z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\ z \left (2 \pi \right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	25.707
25656	19816	\begin{align*} \left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \\ \end{align*}	✓	✓	✓	✓	25.715
25657	4802	\begin{align*} x y^{\prime }+2 y&=a \,x^{2 k} y^{k} \\ \end{align*}	✓	✓	✓	✓	25.773
25658	11484	\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	25.794
25659	5265	\begin{align*} x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime }&=\left (a x +2 y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	25.797
25660	13474	\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \\ \end{align*}	✗	✗	✗	✗	25.814
25661	20011	\begin{align*} {y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \\ \end{align*}	✓	✓	✗	✗	25.817
25662	13560	\begin{align*} y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\ \end{align*}	✗	✓	✓	✗	25.826
25663	20964	\begin{align*} y^{\prime }&=\frac {x +y+1}{x +2}-{\mathrm e}^{\frac {x +y+1}{x +2}} \\ \end{align*}	✓	✓	✓	✗	25.829
25664	12860	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a&=0 \\ \end{align*}	✗	✗	✗	✗	25.837
25665	24285	\begin{align*} x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	25.851
25666	18596	\begin{align*} \frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{y^{3}+3 x^{2} y}&=1 \\ \end{align*}	✓	✓	✓	✓	25.856
25667	4324	\begin{align*} y^{\prime }&=\left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 y x +1 \\ \end{align*}	✓	✓	✓	✓	25.869
25668	18879	\begin{align*} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y&=4 t^{2} \\ \end{align*}	✓	✓	✓	✓	25.901
25669	8678	\begin{align*} y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	25.947
25670	13966	\begin{align*} \frac {1+2 y x}{y}+\frac {\left (-x +y\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	25.983
25671	5879	\begin{align*} b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	25.994
25672	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*}	✓	✓	✓	✓	25.997
25673	6361	\begin{align*} y^{\prime \prime }&=a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	26.001
25674	13970	\begin{align*} 6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	26.004
25675	25505	\begin{align*} y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 y t +6 y^{2}} \\ \end{align*}	✓	✓	✓	✗	26.016
25676	25444	\begin{align*} y^{\prime }&=2 y-{\mathrm e}^{i t} \\ \end{align*}	✓	✓	✓	✓	26.019
25677	25485	\begin{align*} y^{\prime }&=\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	26.020
25678	12008	\begin{align*} y^{\prime }&=-\frac {a b y-b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \\ \end{align*}	✓	✓	✓	✗	26.027
25679	6567	\begin{align*} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	26.072
25680	14867	\begin{align*} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x&=0 \\ \end{align*}	✗	✗	✗	✗	26.088
25681	25051	\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	26.089
25682	8695	\begin{align*} x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\ \end{align*}	✓	✓	✓	✓	26.126
25683	12066	\begin{align*} y^{\prime }&=\frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 x y \ln \left (x \right )+\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	26.126
25684	20821	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	26.129
25685	9156	\begin{align*} y^{\prime }&=\frac {x +y+4}{x -y-6} \\ \end{align*}	✓	✓	✓	✓	26.139
25686	11658	\begin{align*} \left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	26.139
25687	24346	\begin{align*} x -4 y-9+\left (4 x +y-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	26.165
25688	17319	\begin{align*} 3 t +\left (t -4 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	26.168
25689	11608	\begin{align*} x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	26.181
25690	2347	\begin{align*} y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	26.187
25691	21814	\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*}	✓	✓	✓	✓	26.224
25692	22982	\begin{align*} z^{\prime }-z \sin \left (x \right )&={\mathrm e}^{-\cos \left (x \right )} \\ z \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	26.236
25693	19950	\begin{align*} y y^{\prime }+x&=m \left (x y^{\prime }-y\right ) \\ \end{align*}	✓	✓	✓	✗	26.259
25694	21816	\begin{align*} \sin \left (x \right )+\sin \left (y\right )+\left (x \cos \left (y\right )+\cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	26.273
25695	25183	\begin{align*} 3 t^{2} y^{\prime \prime }+2 t y^{\prime }+y&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✗	26.277
25696	2884	\begin{align*} x^{2}+y^{2}&=2 x y y^{\prime } \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	26.293
25697	26321	\begin{align*} \frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	26.297
25698	18499	\begin{align*} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{3} \\ \end{align*}	✓	✓	✗	✓	26.310
25699	5230	\begin{align*} \left (x^{2}+2 y x -y^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	26.311
25700	11550	\begin{align*} x \left (y x -2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	26.312