2.3.222 Problems 22101 to 22200

Table 2.975: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
22101	21510	\begin{align*} y^{\prime }-y&=3 x^{2}+x \\ \end{align*}	✓	✓	✓	✓	5.480
22102	8692	\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}	✓	✓	✓	✓	5.482
22103	12286	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	5.482
22104	12010	\begin{align*} y^{\prime }&=\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.483
22105	3409	\begin{align*} y^{\prime }&=y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	5.484
22106	15620	\begin{align*} y^{\prime }&=y^{3} \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.484
22107	12386	\begin{align*} y^{\prime \prime } x +\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.485
22108	2979	\begin{align*} y+2 \left (x -2 y^{2}\right ) y^{\prime }&=0 \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	5.486
22109	13904	\begin{align*} x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	5.487
22110	3268	\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2}&=2 \\ \end{align*}	✓	✓	✓	✗	5.490
22111	1658	\begin{align*} y^{\prime }&=\frac {x +2 y}{2 x +y} \\ \end{align*}	✓	✓	✓	✓	5.493
22112	17222	\begin{align*} \left (t +3\right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (t +3\right ) \cos \left (t +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.495
22113	14480	\begin{align*} 2 x^{2}+2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.496
22114	19946	\begin{align*} y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \\ \end{align*}	✓	✓	✓	✓	5.497
22115	19800	\begin{align*} 3 y^{2} y^{\prime }+y^{3}&=x -1 \\ \end{align*}	✓	✓	✓	✓	5.502
22116	25028	\begin{align*} y+2 t +2 t y y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	5.502
22117	8380	\begin{align*} y^{\prime } x&=y^{2}-y \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.503
22118	24203	\begin{align*} x y^{2}+y-x +x \left (y x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.505
22119	11331	\begin{align*} y^{\prime }-x y^{2}-3 y x&=0 \\ \end{align*}	✓	✓	✓	✓	5.506
22120	1624	\begin{align*} y^{\prime }&=3 x \left (y-1\right )^{{1}/{3}} \\ y \left (3\right ) &= -7 \\ \end{align*}	✓	✓	✓	✗	5.510
22121	15363	\begin{align*} y^{\prime } y&=\sqrt {y^{2}+x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	5.510
22122	7511	\begin{align*} y^{\prime }&=\frac {2 y}{x}-y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	5.513
22123	14478	\begin{align*} 3 x -y-\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.513
22124	5237	\begin{align*} \left (1-3 x -y\right )^{2} y^{\prime }&=\left (1-2 y\right ) \left (3-6 x -4 y\right ) \\ \end{align*}	✓	✓	✓	✗	5.516
22125	2877	\begin{align*} y^{2}+x^{2}&=x y^{\prime } y \\ \end{align*}	✓	✓	✓	✓	5.523
22126	13270	\begin{align*} x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x&=0 \\ \end{align*}	✓	✓	✓	✗	5.523
22127	19347	\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	5.523
22128	5867	\begin{align*} \left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.530
22129	11509	\begin{align*} y^{\prime } y-{\mathrm e}^{\frac {x}{y}} x&=0 \\ \end{align*}	✓	✓	✓	✓	5.531
22130	9057	\begin{align*} 2 x y^{\prime } y&=y^{2}+x^{2} \\ \end{align*}	✓	✓	✓	✓	5.534
22131	13272	\begin{align*} \left (a \,x^{2}+b x +e \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	5.539
22132	25040	\begin{align*} y^{\prime }&=\frac {t -y}{t +y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	5.539
22133	21512	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{3}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	5.543
22134	2879	\begin{align*} y^{\prime } x +y&=2 \sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	5.546
22135	7846	\begin{align*} y^{\prime } y+x&=0 \\ \end{align*}	✓	✓	✓	✓	5.546
22136	13659	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x} \\ \end{align*}	✓	✓	✓	✗	5.546
22137	11983	\begin{align*} y^{\prime }&=\frac {1}{x \left (x y^{2}+1+x \right ) y} \\ \end{align*}	✓	✓	✓	✓	5.548
22138	4350	\begin{align*} 2 y^{2} x^{2}+y+\left (x^{3} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.549
22139	24124	\begin{align*} m y-n x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.554
22140	17225	\begin{align*} 2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.555
22141	21538	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	5.556
22142	8703	\begin{align*} x +y-\left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.557
22143	2914	\begin{align*} 3 x +y+\left (x +3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.563
22144	11526	\begin{align*} \left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \\ \end{align*}	✓	✓	✓	✓	5.563
22145	13569	\begin{align*} y^{\prime } y+x \left (a \,x^{2}+b \right ) y+x&=0 \\ \end{align*}	✗	✓	✓	✗	5.563
22146	7390	\begin{align*} x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \\ \end{align*}	✓	✓	✓	✓	5.564
22147	5598	\begin{align*} a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.566
22148	5657	\begin{align*} y {y^{\prime }}^{3}-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.567
22149	7856	\begin{align*} 1+2 y+\left (-x^{2}+4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.572
22150	18068	\begin{align*} \left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\ \end{align*}	✓	✓	✓	✓	5.576
22151	18493	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (2 x \right ) \\ y \left (0\right ) &= -\sqrt {3} \\ \end{align*}	✓	✓	✗	✓	5.576
22152	22580	\begin{align*} y^{\prime }&=\frac {x +3 y}{x -3 y} \\ \end{align*}	✓	✓	✓	✗	5.577
22153	12365	\begin{align*} y^{\prime \prime } x -y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.585
22154	13379	\begin{align*} y^{\prime }&=y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	5.586
22155	24190	\begin{align*} 1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.587
22156	14040	\begin{align*} 1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.590
22157	3010	\begin{align*} 6+2 y&=x y^{\prime } y \\ \end{align*}	✓	✓	✓	✓	5.603
22158	7933	\begin{align*} 2 x y^{5}-y+2 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.606
22159	23903	\begin{align*} y+2 x^{3}+\left (2 x -\frac {x^{4}}{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.607
22160	2357	\begin{align*} y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\ y \left (0\right ) &= 100 \\ \end{align*}	✓	✓	✓	✓	5.608
22161	2333	\begin{align*} {\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.609
22162	20548	\begin{align*} y^{\prime \prime }&={\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.609
22163	5680	\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.610
22164	4429	\begin{align*} 2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.612
22165	19270	\begin{align*} x y^{\prime } y&=\left (x +1\right ) \left (1+y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.613
22166	25715	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✗	5.615
22167	8818	\begin{align*} y+\sqrt {y^{2}+x^{2}}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.616
22168	13261	\begin{align*} \left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 y x +\left (-a +1\right ) x^{2}-b&=0 \\ \end{align*}	✓	✓	✓	✗	5.616
22169	23844	\begin{align*} \left (x +y+1\right ) y^{\prime }&=x +y+2 \\ \end{align*}	✓	✓	✓	✓	5.616
22170	12032	\begin{align*} y^{\prime }&=\frac {\left (x^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	5.626
22171	22551	\begin{align*} y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x -y\right )} \\ \end{align*}	✓	✓	✓	✓	5.626
22172	21579	\begin{align*} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=f \left (x \right ) \\ y \left (x_{0} \right ) &= y_{0} \\ y^{\prime }\left (x_{0} \right ) &= y_{1} \\ \end{align*}	✓	✓	✓	✓	5.630
22173	11956	\begin{align*} y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x} \\ \end{align*}	✓	✓	✓	✗	5.635
22174	17910	\begin{align*} y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\ \end{align*}	✓	✓	✓	✗	5.636
22175	6811	\begin{align*} \sqrt {1+{y^{\prime \prime }}^{2}}\, \left (1-y^{\prime \prime \prime }\right )&=y^{\prime \prime } y^{\prime \prime \prime } \\ \end{align*}	✓	✓	✓	✓	5.637
22176	22398	\begin{align*} 2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	5.637
22177	14019	\begin{align*} y^{\prime } x +y+{\mathrm e}^{x} x^{4} y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	5.638
22178	7027	\begin{align*} y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.642
22179	7218	\begin{align*} x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✗	5.645
22180	7751	\begin{align*} x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.646
22181	17887	\begin{align*} {\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.646
22182	12639	\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+a \right ) y^{\prime }}{x \left (x^{2}+a \right )}-\frac {b y}{x^{2} \left (x^{2}+a \right )} \\ \end{align*}	✓	✓	✓	✗	5.647
22183	22387	\begin{align*} x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.647
22184	17212	\begin{align*} 2 t y+\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.648
22185	7396	\begin{align*} y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\ y \left (0\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✗	✓	5.653
22186	17336	\begin{align*} y-t y^{\prime }&=2 y^{2} \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	5.669
22187	12076	\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )} \\ \end{align*}	✓	✓	✓	✗	5.670
22188	21787	\begin{align*} x^{\prime \prime }&=4 x^{3}-4 x \\ \end{align*}	✓	✓	✓	✗	5.672
22189	2873	\begin{align*} y^{\prime }&=\frac {2 x -y}{x +4 y} \\ \end{align*}	✓	✓	✓	✓	5.675
22190	7314	\begin{align*} {y^{\prime \prime }}^{2}&=k^{2} \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	5.678
22191	23196	\begin{align*} y+\left (2 x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.679
22192	2900	\begin{align*} x -y+1+\left (x -y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.682
22193	8290	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (3\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.687
22194	7515	\begin{align*} r^{\prime }&=r^{2}+\frac {2 r}{t} \\ \end{align*}	✓	✓	✓	✓	5.691
22195	16353	\begin{align*} x y^{\prime } y&=2 y^{2}+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	5.694
22196	24211	\begin{align*} y \left (x^{4}-y^{2}\right )+x \left (x^{4}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.694
22197	13656	\begin{align*} y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\ \end{align*}	✗	✓	✓	✗	5.696
22198	13554	\begin{align*} y^{\prime } y&=\left (a x +b \right ) y+1 \\ \end{align*}	✗	✓	✓	✗	5.697
22199	19948	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	5.697
22200	13358	\begin{align*} y^{\prime }&=a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\ \end{align*}	✓	✓	✓	✗	5.698