2.3.243 Problems 24201 to 24300

Table 2.1035: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
24201	14466	\begin{align*} v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.566
24202	25708	\begin{align*} y^{\prime }&=\sqrt {y x} \\ \end{align*}	✓	✓	✓	✓	20.569
24203	2894	\begin{align*} x +\left (x -2 y+2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.572
24204	5060	\begin{align*} \left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	20.573
24205	11799	\begin{align*} \sin \left (y\right ) {y^{\prime }}^{2}+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4}&=0 \\ \end{align*}	✓	✗	✓	✗	20.573
24206	19069	\begin{align*} y^{\prime }&=\frac {2 y x}{x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	20.593
24207	18285	\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\ y \left (-\infty \right ) &= 3 \\ \end{align*}	✗	✓	✗	✓	20.605
24208	11490	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {-1+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	20.637
24209	24181	\begin{align*} v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\ v \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	20.638
24210	23883	\begin{align*} 2 x +2 y-3+\left (1-2 y+2 x \right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	20.643
24211	7490	\begin{align*} \left (y-4 x -1\right )^{2}-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.644
24212	9018	\begin{align*} y^{\prime }&=\frac {x -y+2}{x +y-1} \\ \end{align*}	✓	✓	✓	✓	20.664
24213	6414	\begin{align*} x^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {y}{\sqrt {x}}\right ) \\ \end{align*}	✗	✓	✓	✗	20.671
24214	6814	\begin{align*} y^{\prime }&=\frac {x y}{x^{2}-y^{2}} \\ \end{align*}	✓	✓	✓	✓	20.671
24215	18879	\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \\ \end{align*}	✓	✓	✓	✓	20.671
24216	17111	\begin{align*} y^{\prime }&=\frac {\sqrt {t}}{y} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	20.672
24217	25714	\begin{align*} \left (-x +y\right ) y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	20.691
24218	3647	\begin{align*} 2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	20.695
24219	17224	\begin{align*} -\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.698
24220	7955	\begin{align*} y&=2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✓	20.718
24221	4407	\begin{align*} 2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.745
24222	14465	\begin{align*} 2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.792
24223	17914	\begin{align*} y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✓	20.793
24224	20120	\begin{align*} \sqrt {x}\, y^{\prime \prime }+2 y^{\prime } x +3 y&=x \\ \end{align*}	✗	✓	✓	✗	20.802
24225	17920	\begin{align*} x +y-2+\left (x -y+4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.831
24226	2886	\begin{align*} {\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	20.838
24227	7392	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	20.887
24228	12935	\begin{align*} y y^{\prime \prime }-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	20.926
24229	6244	\begin{align*} \left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	20.931
24230	7700	\begin{align*} x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	20.936
24231	7115	\begin{align*} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	20.967
24232	21596	\begin{align*} y^{\prime }&=\frac {2 x +y}{y} \\ \end{align*}	✓	✓	✓	✓	20.970
24233	15289	\begin{align*} x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	20.974
24234	22383	\begin{align*} x +2+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	20.974
24235	17841	\begin{align*} y^{\prime }&=\sqrt {x^{2}-y}-x \\ \end{align*}	✓	✓	✓	✗	20.986
24236	5167	\begin{align*} x \left (x -2 y\right ) y^{\prime }+y \left (2 x -y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	20.988
24237	3640	\begin{align*} -y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	20.999
24238	14550	\begin{align*} x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.010
24239	3034	\begin{align*} 2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	21.021
24240	24298	\begin{align*} \sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	21.044
24241	7895	\begin{align*} x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.049
24242	8230	\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	21.049
24243	6330	\begin{align*} b y+a \left (-1+y^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	21.056
24244	12454	\begin{align*} x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\ \end{align*}	✗	✓	✓	✗	21.061
24245	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*}	✓	✓	✓	✓	21.063
24246	18057	\begin{align*} 1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	21.072
24247	17038	\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	21.086
24248	4189	\begin{align*} y y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	21.092
24249	11851	\begin{align*} y \ln \left (y^{\prime }\right )+y^{\prime }-\ln \left (y\right ) y-y x&=0 \\ \end{align*}	✓	✓	✓	✓	21.124
24250	11945	\begin{align*} y^{\prime }&=\frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y} \\ \end{align*}	✓	✓	✓	✗	21.125
24251	21852	\begin{align*} 3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.142
24252	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*}	✓	✓	✓	✗	21.181
24253	11361	\begin{align*} y^{\prime }-\frac {\sqrt {-1+y^{2}}}{\sqrt {x^{2}-1}}&=0 \\ \end{align*}	✓	✓	✓	✓	21.183
24254	24828	\begin{align*} y&=y^{\prime } x +x^{3} {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	21.183
24255	15453	\begin{align*} x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \\ \end{align*}	✓	✓	✓	✓	21.201
24256	22587	\begin{align*} 3 y^{2}+4 y x +\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.204
24257	21764	\begin{align*} y^{\prime \prime }-\frac {2 {y^{\prime }}^{2}}{y}-y&=0 \\ \end{align*}	✓	✓	✓	✗	21.210
24258	16292	\begin{align*} y^{\prime }&=\frac {x -y}{x +y} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	21.211
24259	5169	\begin{align*} x \left (1-x -2 y\right ) y^{\prime }+\left (2 x +y+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	21.213
24260	21087	\begin{align*} x^{\prime }&=\frac {t^{2}+x^{2}}{2 t x} \\ \end{align*}	✓	✓	✓	✓	21.243
24261	4240	\begin{align*} x^{2}-y^{2}+y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	21.261
24262	2888	\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\ y \left (6\right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	21.276
24263	19716	\begin{align*} y^{2}&=x \left (-x +y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	21.276
24264	14537	\begin{align*} y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	21.299
24265	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*}	✓	✓	✓	✓	21.313
24266	7504	\begin{align*} y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\ \end{align*}	✓	✓	✓	✓	21.313
24267	23198	\begin{align*} y-\left (x -2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.339
24268	16324	\begin{align*} y+\left (y^{4}-3 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.348
24269	11984	\begin{align*} y^{\prime }&=\frac {2 x \,{\mathrm e}^{x}-2 x -\ln \left (x \right )-1+x^{4} \ln \left (x \right )+x^{4}-2 y \ln \left (x \right ) x^{2}-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1} \\ \end{align*}	✓	✓	✓	✗	21.350
24270	24296	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ y \left (0\right ) &= \frac {\sqrt {3}}{2} \\ \end{align*}	✓	✓	✓	✗	21.372
24271	14016	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	21.390
24272	15155	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+y^{\prime } x +7 y&=1 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	21.411
24273	26394	\begin{align*} x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.421
24274	1752	\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	21.422
24275	11914	\begin{align*} y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\ \end{align*}	✓	✓	✓	✓	21.450
24276	2770	\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	21.452
24277	2771	\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t} \\ x_{3}^{\prime }&=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	21.462
24278	3229	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	21.462
24279	5780	\begin{align*} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.472
24280	26367	\begin{align*} y&=2 y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	21.479
24281	6997	\begin{align*} \left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \\ \end{align*}	✓	✓	✓	✓	21.485
24282	4829	\begin{align*} y^{\prime } x&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \\ \end{align*}	✓	✓	✓	✓	21.501
24283	6833	\begin{align*} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.526
24284	5168	\begin{align*} x \left (x -2 y+1\right ) y^{\prime }+\left (1-2 x +y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	21.550
24285	17991	\begin{align*} {y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{2 x}-1\right ) \\ \end{align*}	✓	✓	✓	✓	21.552
24286	5264	\begin{align*} 2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\ \end{align*}	✓	✓	✓	✓	21.571
24287	3007	\begin{align*} x -2 y+1+\left (-2+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	21.579
24288	12232	\begin{align*} y^{\prime }&=-\frac {-y+x^{2} \sqrt {x^{2}+y^{2}}-x \sqrt {x^{2}+y^{2}}\, y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x} \\ \end{align*}	✗	✓	✓	✗	21.617
24289	18610	\begin{align*} 5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\ \end{align*}	✓	✓	✓	✓	21.627
24290	23878	\begin{align*} y^{\prime }&=\frac {2 y^{3}+2 x^{2} y}{x^{3}+2 x y^{2}} \\ \end{align*}	✓	✓	✓	✗	21.627
24291	19813	\begin{align*} \left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	21.639
24292	19389	\begin{align*} y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	21.648
24293	24061	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	21.648
24294	21985	\begin{align*} y^{\prime }&=2 \sqrt {{| y|}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	21.650
24295	18614	\begin{align*} y^{\prime }&=a y+b y^{3} \\ \end{align*}	✓	✓	✓	✓	21.691
24296	9166	\begin{align*} y^{\prime }&=\frac {x^{2}-y x}{y^{2} \cos \left (\frac {x}{y}\right )} \\ \end{align*}	✓	✓	✓	✗	21.715
24297	24388	\begin{align*} y^{\prime } x&=x^{3} y^{3}-2 y \\ \end{align*}	✓	✓	✓	✓	21.727
24298	3776	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	21.728
24299	21394	\begin{align*} y y^{\prime } x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	21.731
24300	12568	\begin{align*} -y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	21.800