2.3.255 Problems 25401 to 25500

Table 2.1083: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
25401	23958	\begin{align*} x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	22.293
25402	14474	\begin{align*} x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \\ y \left (2\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	22.297
25403	21036	\begin{align*} x^{\prime }&=\sin \left (x\right ) \\ \end{align*}	✓	✓	✓	✗	22.309
25404	2339	\begin{align*} \sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	22.312
25405	9206	\begin{align*} 2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	22.325
25406	18561	\begin{align*} y^{3}+y^{\prime }&=0 \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	22.333
25407	2554	\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	22.359
25408	4966	\begin{align*} \left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	22.363
25409	1601	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	22.372
25410	9179	\begin{align*} y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\ \end{align*}	✓	✓	✓	✗	22.400
25411	12854	\begin{align*} y^{\prime \prime }&=\frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \\ \end{align*}	✗	✓	✓	✗	22.408
25412	11842	\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+{y^{\prime }}^{2} x +y&=0 \\ \end{align*}	✓	✓	✓	✗	22.423
25413	12560	\begin{align*} \operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	22.424
25414	2503	\begin{align*} \left (t -\sqrt {y t}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	22.451
25415	23887	\begin{align*} \frac {1-6 x^{2} y}{x}+\frac {\left (2+5 y-3 x^{2} y\right ) y^{\prime }}{y}&=0 \\ \end{align*}	✓	✓	✓	✗	22.454
25416	24399	\begin{align*} y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\cos \left (x \right ) \sec \left (y\right ) \\ \end{align*}	✗	✓	✓	✓	22.465
25417	27545	\begin{align*} y^{4}-y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	22.477
25418	5203	\begin{align*} x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\ \end{align*}	✓	✓	✓	✓	22.490
25419	6873	\begin{align*} \frac {\sqrt {f \,x^{4}+x^{3} c +c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}&=-1 \\ \end{align*}	✓	✓	✓	✓	22.500
25420	5129	\begin{align*} x y y^{\prime }+2 x^{2}-2 y x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	22.504
25421	19389	\begin{align*} y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	22.507
25422	13980	\begin{align*} x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	22.524
25423	15602	\begin{align*} x -y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	22.604
25424	17991	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{2 x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	22.619
25425	14084	\begin{align*} 8 \left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\ \end{align*}	✓	✓	✓	✗	22.626
25426	14506	\begin{align*} x y^{\prime }+y&=\left (y x \right )^{{3}/{2}} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	22.630
25427	15350	\begin{align*} x +y+\left (-x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	22.634
25428	5212	\begin{align*} y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	22.639
25429	5247	\begin{align*} \left (x^{2}+a y^{2}\right ) y^{\prime }&=y x \\ \end{align*}	✓	✓	✓	✓	22.651
25430	22076	\begin{align*} y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	22.706
25431	14468	\begin{align*} \left (2 s^{2}+2 t s+t^{2}\right ) s^{\prime }+s^{2}+2 t s-t^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	22.707
25432	13639	\begin{align*} y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\ \end{align*}	✗	✓	✓	✗	22.721
25433	18335	\begin{align*} 4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \\ y \left (\infty \right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	22.739
25434	21756	\begin{align*} 2 x^{4} y y^{\prime }+y^{4}&=4 x^{6} \\ \end{align*}	✓	✓	✓	✗	22.745
25435	10119	\begin{align*} y^{\prime \prime }-x^{3} y-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	22.784
25436	8950	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	22.786
25437	13640	\begin{align*} y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	22.800
25438	7740	\begin{align*} x^{2} y^{\prime }&=y^{2}-x y y^{\prime } \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	22.902
25439	9762	\begin{align*} y&=x y^{\prime }+x^{3} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	22.909
25440	20153	\begin{align*} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \\ \end{align*}	✗	✗	✗	✗	22.926
25441	8949	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	22.941
25442	13794	\begin{align*} x^{2} y^{\prime \prime }+a x y^{\prime }+x^{n} \left (b \,x^{n}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	22.941
25443	19812	\begin{align*} \left (x^{2}+3 y x -y^{2}\right ) y^{\prime }-3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	22.998
25444	17272	\begin{align*} y^{\prime }&=\frac {t +4 y}{4 t +y} \\ \end{align*}	✓	✓	✓	✓	23.000
25445	17214	\begin{align*} \sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.070
25446	27690	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	23.088
25447	2888	\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\ y \left (6\right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	23.092
25448	27243	\begin{align*} x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	23.101
25449	4891	\begin{align*} x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\ \end{align*}	✗	✓	✓	✗	23.125
25450	23761	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=\ln \left (x \right ) \\ y \left (1\right ) &= A \\ y \left (2\right ) &= B \\ \end{align*}	✓	✓	✓	✓	23.132
25451	5358	\begin{align*} {y^{\prime }}^{2}+x^{2}&=4 y \\ \end{align*}	✓	✓	✓	✗	23.136
25452	27695	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=10 x \\ \end{align*}	✓	✓	✓	✓	23.139
25453	6907	\begin{align*} y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	23.149
25454	22428	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	23.158
25455	22034	\begin{align*} y \sin \left (x \right )+y \cos \left (x \right ) x +\left (x \sin \left (x \right )+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.178
25456	11498	\begin{align*} y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	23.190
25457	140	\begin{align*} 1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	23.193
25458	25188	\begin{align*} y^{\prime \prime }+2 y^{\prime }+\sin \left (t \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	23.202
25459	27475	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.211
25460	12044	\begin{align*} y^{\prime }&=-\frac {\left (x \ln \left (y\right )+\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✓	23.225
25461	16315	\begin{align*} 2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.250
25462	22382	\begin{align*} x^{2}-y^{2}-2 x y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.269
25463	13811	\begin{align*} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y&=0 \\ \end{align*}	✗	✓	✓	✗	23.290
25464	17045	\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	23.329
25465	12403	\begin{align*} 4 x y^{\prime \prime }+4 y-\left (x +2\right ) y+l y&=0 \\ \end{align*}	✗	✓	✓	✗	23.340
25466	25717	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (2\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	23.355
25467	24972	\begin{align*} y^{\prime }&=4 t y^{2} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	23.362
25468	18054	\begin{align*} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	23.363
25469	24322	\begin{align*} \left (3 \tan \left (x \right )-2 \cos \left (y\right )\right ) \sec \left (x \right )^{2}+\tan \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	23.374
25470	20690	\begin{align*} y^{\prime }+x \sin \left (2 y\right )&=x^{3} \cos \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✗	23.375
25471	19278	\begin{align*} x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\ \end{align*}	✓	✓	✓	✓	23.412
25472	8870	\begin{align*} y^{\prime }+3 y&={\mathrm e}^{i x} \\ \end{align*}	✓	✓	✓	✓	23.418
25473	17841	\begin{align*} y^{\prime }&=\sqrt {x^{2}-y}-x \\ \end{align*}	✓	✓	✓	✗	23.424
25474	7472	\begin{align*} 5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	23.428
25475	19373	\begin{align*} x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✗	23.434
25476	21042	\begin{align*} x^{\prime }&=\left (x+2\right ) \left (1-x^{4}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	23.454
25477	2345	\begin{align*} 3 y t +y^{2}+\left (t^{2}+y t \right ) y^{\prime }&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	23.456
25478	19813	\begin{align*} \left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	23.458
25479	4421	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.467
25480	5467	\begin{align*} {y^{\prime }}^{2} x -\left (3 x -y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	23.473
25481	16231	\begin{align*} y^{\prime }&=\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	23.487
25482	22566	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.494
25483	25484	\begin{align*} y^{\prime }&=a y-y^{3} \\ \end{align*}	✓	✓	✓	✓	23.509
25484	6003	\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=a -x +x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	23.539
25485	5068	\begin{align*} \left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	23.540
25486	11511	\begin{align*} \left (y+1\right ) y^{\prime }-y-x&=0 \\ \end{align*}	✓	✓	✓	✗	23.541
25487	17291	\begin{align*} y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	23.554
25488	24183	\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.576
25489	5415	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✗	23.588
25490	17920	\begin{align*} x +y-2+\left (x -y+4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.595
25491	24202	\begin{align*} 2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	23.599
25492	2872	\begin{align*} x y^{\prime }-y&=\sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	23.621
25493	5422	\begin{align*} {y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \\ \end{align*}	✓	✓	✓	✗	23.668
25494	15834	\begin{align*} \theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\ \end{align*}	✓	✓	✓	✓	23.684
25495	4247	\begin{align*} y^{\prime }&=\frac {x +y+4}{x -y-6} \\ \end{align*}	✓	✓	✓	✓	23.691
25496	6881	\begin{align*} x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\ \end{align*}	✓	✓	✓	✓	23.694
25497	13395	\begin{align*} y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	23.705
25498	17307	\begin{align*} t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	23.707
25499	12450	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	23.735
25500	17308	\begin{align*} y^{\prime }&=\frac {-t^{2}+y^{2}}{y t} \\ y \left (4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	23.763