2.3.203 Problems 20201 to 20300

Table 2.949: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20201	21872	\begin{align*} y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	5.461
20202	13785	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\left (n +\frac {1}{2}\right )^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	5.463
20203	1567	\begin{align*} y^{\prime } x +2 y&=8 x^{2} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.467
20204	1648	\begin{align*} y^{\prime }&=\frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 y x} \\ \end{align*}	✓	✓	✓	✓	5.470
20205	9658	\begin{align*} x^{\prime }&=x-y+z+t -1 \\ y^{\prime }&=2 x+y-z-3 t^{2} \\ z^{\prime }&=x+y+z+t^{2}-t +2 \\ \end{align*}	✓	✓	✓	✓	5.470
20206	19933	\begin{align*} y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\ \end{align*}	✓	✓	✓	✓	5.471
20207	22598	\begin{align*} y^{\prime }&=\tan \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	5.473
20208	22177	\begin{align*} \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\ \end{align*} Series expansion around \(x=-1\).	✓	✓	✓	✓	5.474
20209	22210	\begin{align*} x^{2} y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } x +\left (x^{3}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	5.475
20210	5539	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	5.477
20211	7510	\begin{align*} y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\ \end{align*}	✓	✓	✓	✓	5.477
20212	23054	\begin{align*} s^{\prime \prime }&=-9 s \\ s \left (0\right ) &= 9 \\ s^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.477
20213	16221	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	5.479
20214	7861	\begin{align*} y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (-y^{\prime } x +y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.482
20215	4997	\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 y x \right ) y \\ \end{align*}	✓	✓	✓	✓	5.483
20216	2836	\begin{align*} y^{\prime \prime }-\lambda y&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.484
20217	10319	\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	5.488
20218	1688	\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (x^{2}+8 y x +18 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.490
20219	16339	\begin{align*} 4 y x -6+x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.492
20220	21061	\begin{align*} x^{\prime }&=4 t^{3} \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	5.493
20221	22964	\begin{align*} y^{\prime }&=\frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	5.494
20222	10405	\begin{align*} y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	5.495
20223	8398	\begin{align*} \left (\sqrt {x}+x \right ) y^{\prime }&=\sqrt {y}+y \\ \end{align*}	✓	✓	✓	✓	5.496
20224	13233	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b \,x^{m} y+x^{m} b c -a \,c^{2} x^{n} \\ \end{align*}	✓	✓	✓	✗	5.500
20225	14220	\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	5.500
20226	19318	\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.500
20227	3663	\begin{align*} y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	5.503
20228	19286	\begin{align*} y^{\prime }&=\sin \left (x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.504
20229	24968	\begin{align*} y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.504
20230	4434	\begin{align*} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\ \end{align*}	✓	✓	✓	✓	5.507
20231	7531	\begin{align*} y^{\prime }+\frac {2 y}{x}&=2 y^{2} x^{2} \\ \end{align*}	✓	✓	✓	✓	5.507
20232	11640	\begin{align*} y^{\prime } \left (1+\sin \left (x \right )\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.507
20233	14238	\begin{align*} x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.507
20234	15868	\begin{align*} y^{\prime }&=\cos \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.508
20235	15921	\begin{align*} y^{\prime }&=-\frac {y}{1+t}+2 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	5.511
20236	23013	\begin{align*} y^{\prime \prime }-3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	5.511
20237	4199	\begin{align*} \left (x^{3}+x \right ) y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	5.513
20238	14075	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\ \end{align*}	✓	✓	✓	✓	5.513
20239	7246	\begin{align*} 2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.517
20240	11374	\begin{align*} y^{\prime }-\left (\frac {a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3}}\right )^{{2}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	5.517
20241	22996	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{k x} \\ \end{align*}	✓	✓	✓	✓	5.520
20242	5531	\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\ \end{align*}	✓	✓	✓	✗	5.523
20243	23371	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.526
20244	5365	\begin{align*} {y^{\prime }}^{2}&=a +b y^{2} \\ \end{align*}	✓	✓	✓	✓	5.527
20245	13796	\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	5.527
20246	17273	\begin{align*} t -y+y^{\prime } t&=0 \\ \end{align*}	✓	✓	✓	✓	5.530
20247	24292	\begin{align*} a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\ \end{align*}	✓	✓	✓	✓	5.530
20248	17978	\begin{align*} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.532
20249	20948	\begin{align*} y^{\prime }&=k y-c y^{2} \\ y \left (0\right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	5.533
20250	21458	\begin{align*} y^{\prime }+y x&=x y^{2} \\ \end{align*}	✓	✓	✓	✓	5.533
20251	5480	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	5.535
20252	15345	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}-\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	5.537
20253	17219	\begin{align*} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	5.537
20254	4846	\begin{align*} \left (a +x \right ) y^{\prime }&=-b -c y \\ \end{align*}	✓	✓	✓	✓	5.538
20255	6915	\begin{align*} 7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.538
20256	17151	\begin{align*} y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \\ \end{align*}	✓	✓	✓	✓	5.538
20257	4679	\begin{align*} y^{\prime }&=x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	5.540
20258	20573	\begin{align*} a y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	5.540
20259	4195	\begin{align*} y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	5.542
20260	11333	\begin{align*} y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	5.542
20261	14512	\begin{align*} y^{\prime }+y&=2 \sin \left (x \right )+5 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	5.542
20262	11722	\begin{align*} \left (y^{\prime } x +y+2 x \right )^{2}-4 y x -4 x^{2}-4 a&=0 \\ \end{align*}	✓	✓	✓	✗	5.543
20263	1156	\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \\ \end{align*}	✓	✓	✓	✓	5.547
20264	5091	\begin{align*} \left (x^{3}+2 y\right ) y^{\prime }&=3 x \left (2-y x \right ) \\ \end{align*}	✓	✓	✓	✗	5.550
20265	17998	\begin{align*} {y^{\prime }}^{2}-4 y^{\prime } x +2 y+2 x^{2}&=0 \\ \end{align*}	✓	✓	✗	✓	5.550
20266	16321	\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.551
20267	6012	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{2} \left (x^{2}-1\right ) \\ \end{align*}	✓	✓	✓	✓	5.552
20268	2353	\begin{align*} y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\ y \left (0\right ) &= {\frac {2}{5}} \\ \end{align*}	✗	✗	✗	✗	5.554
20269	14264	\begin{align*} x^{\prime }&=\left (t +x\right )^{2} \\ \end{align*}	✓	✓	✓	✓	5.555
20270	19872	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	5.556
20271	23375	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	5.556
20272	22362	\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.561
20273	25782	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (0\right ) &= -{\frac {5}{2}} \\ \end{align*}	✓	✓	✓	✓	5.561
20274	4722	\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✓	5.565
20275	5612	\begin{align*} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	5.565
20276	14144	\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	5.567
20277	22900	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	5.567
20278	11593	\begin{align*} \left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	5.569
20279	20572	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	5.572
20280	26083	\begin{align*} y^{\prime }&=\frac {x +y-2}{y-x -4} \\ \end{align*}	✓	✓	✓	✓	5.572
20281	14852	\begin{align*} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	5.574
20282	25057	\begin{align*} y^{\prime }&=y^{2} \\ y \left (t_{0} \right ) &= y_{0} \\ \end{align*}	✓	✓	✓	✓	5.574
20283	14031	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\ \end{align*}	✓	✓	✓	✓	5.575
20284	1580	\begin{align*} y^{\prime } x +y^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	5.576
20285	4677	\begin{align*} y^{\prime }&=1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \\ \end{align*}	✓	✓	✓	✓	5.577
20286	7816	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	5.578
20287	11576	\begin{align*} \left (-1+3 x +y\right )^{2} y^{\prime }-\left (-1+2 y\right ) \left (4 y+6 x -3\right )&=0 \\ \end{align*}	✓	✓	✓	✗	5.582
20288	16369	\begin{align*} \left (3-x +y\right )^{2} \left (y^{\prime }-1\right )&=1 \\ \end{align*}	✓	✓	✓	✓	5.584
20289	7332	\begin{align*} x^{2} y^{\prime }-y x&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	5.586
20290	7858	\begin{align*} 1+y-\left (x +1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	5.590
20291	15818	\begin{align*} y^{\prime }&=\left (1+t \right ) y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	5.591
20292	25822	\begin{align*} y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\ \end{align*}	✓	✓	✓	✓	5.594
20293	14007	\begin{align*} \left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	5.595
20294	5315	\begin{align*} x \left (a +y^{3} b x \right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	5.596
20295	20303	\begin{align*} -y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✓	✓	✓	✓	5.596
20296	19258	\begin{align*} y \ln \left (y\right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	5.597
20297	13711	\begin{align*} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	5.601
20298	4918	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y \left (2 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	5.602
20299	20233	\begin{align*} \frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y}&=0 \\ \end{align*}	✓	✓	✓	✓	5.602
20300	13449	\begin{align*} y^{\prime }&=y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	5.605