2.3.203 Problems 20201 to 20300

Table 2.979: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
20201	20177	\begin{align*} a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.489
20202	12117	\begin{align*} y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\ \end{align*}	✗	✗	✗	✗	4.492
20203	14521	\begin{align*} x^{2}-2 y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.492
20204	21353	\begin{align*} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.492
20205	9554	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.493
20206	14220	\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	4.493
20207	14833	\begin{align*} t^{2} x^{\prime \prime }+3 x^{\prime } t +3 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.493
20208	25495	\begin{align*} y^{\prime }&=\frac {y}{t} \\ \end{align*}	✓	✓	✓	✓	4.493
20209	7748	\begin{align*} y^{\prime }+x +x y^{2}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.496
20210	21439	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+4 y x&=x \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.497
20211	25859	\begin{align*} x^{3}+x y^{4}+2 y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.497
20212	17311	\begin{align*} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.498
20213	24974	\begin{align*} 2 y t +y^{\prime }&=0 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	4.499
20214	25039	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.500
20215	25809	\begin{align*} y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\ \end{align*}	✓	✓	✓	✓	4.500
20216	5239	\begin{align*} 3 y^{2} y^{\prime }&=1+x +a y^{3} \\ \end{align*}	✓	✓	✓	✓	4.503
20217	5979	\begin{align*} -a^{2} y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.503
20218	4981	\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=\left (x^{2}-x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	4.504
20219	20500	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	4.505
20220	14194	\begin{align*} x^{\prime }&=-x^{2} \\ \end{align*}	✓	✓	✓	✓	4.506
20221	2968	\begin{align*} x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.507
20222	24281	\begin{align*} y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.507
20223	14963	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.511
20224	60	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.512
20225	5491	\begin{align*} 4 {y^{\prime }}^{2} x +4 y y^{\prime }-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	4.512
20226	7483	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.513
20227	17330	\begin{align*} y t +y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	4.513
20228	21363	\begin{align*} {\mathrm e}^{-y} \left (y^{\prime }+1\right )&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	4.515
20229	17251	\begin{align*} -\frac {y}{2}+y^{\prime }&=\frac {t}{y} \\ \end{align*}	✓	✓	✓	✓	4.517
20230	20576	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	4.518
20231	1143	\begin{align*} y^{\prime }&=\frac {2 x}{1+2 y} \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.519
20232	2343	\begin{align*} 3 t^{2}+4 y t +\left (2 t^{2}+2 y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.520
20233	10235	\begin{align*} y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	4.521
20234	21422	\begin{align*} y^{\prime }&=\frac {-y x +\ln \left (x^{2}\right )}{x^{2}+x \,{\mathrm e}^{y}} \\ \end{align*}	✓	✓	✓	✗	4.523
20235	25651	\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align*}	✗	✗	✗	✗	4.523
20236	26210	\begin{align*} x y y^{\prime }+1+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.523
20237	7395	\begin{align*} \frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.526
20238	18948	\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.526
20239	21761	\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.526
20240	16357	\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\ \end{align*}	✓	✓	✓	✓	4.528
20241	4265	\begin{align*} x y^{\prime }&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	4.530
20242	14906	\begin{align*} T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \\ \end{align*}	✓	✓	✓	✓	4.530
20243	14367	\begin{align*} x^{\prime }+3 x&=\delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right ) \\ x \left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.531
20244	5001	\begin{align*} x^{5} y^{\prime }&=1-3 x^{4} y \\ \end{align*}	✓	✓	✓	✓	4.532
20245	7476	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.532
20246	17472	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.532
20247	8750	\begin{align*} \frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.534
20248	13662	\begin{align*} y^{\prime \prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	4.535
20249	13282	\begin{align*} y^{\prime }&=y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\ \end{align*}	✓	✓	✓	✗	4.538
20250	207	\begin{align*} \left (2 x +1\right ) y^{\prime }+y&=\left (2 x +1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✓	4.539
20251	5372	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.540
20252	17266	\begin{align*} \sqrt {t^{2}+1}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.542
20253	5715	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.543
20254	8676	\begin{align*} y^{\prime }&=\left (-1+y\right ) \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✓	4.543
20255	8984	\begin{align*} 3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.543
20256	4965	\begin{align*} x \left (a x +1\right ) y^{\prime }+a -y&=0 \\ \end{align*}	✓	✓	✓	✓	4.544
20257	11508	\begin{align*} y y^{\prime }+x y^{2}-4 x&=0 \\ \end{align*}	✓	✓	✓	✓	4.544
20258	2847	\begin{align*} \left (x +1\right ) y^{\prime }-1+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.547
20259	6456	\begin{align*} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.549
20260	4287	\begin{align*} y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\ \end{align*}	✓	✓	✓	✓	4.550
20261	13354	\begin{align*} y^{\prime }&=y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m} \\ \end{align*}	✓	✓	✓	✗	4.550
20262	17286	\begin{align*} t +y-t y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.550
20263	19899	\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.550
20264	19401	\begin{align*} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.552
20265	22251	\begin{align*} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (-4+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	4.552
20266	8735	\begin{align*} 2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.553
20267	20545	\begin{align*} -a^{2} y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.553
20268	3476	\begin{align*} y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	4.554
20269	11377	\begin{align*} y^{\prime }-a \cos \left (y\right )+b&=0 \\ \end{align*}	✓	✓	✓	✗	4.554
20270	11463	\begin{align*} 2 x^{2} y^{\prime }-2 y^{2}-3 y x +2 a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✗	4.555
20271	22028	\begin{align*} y+2 x y^{3}+\left (1+3 x^{2} y^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.556
20272	18809	\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	4.558
20273	7506	\begin{align*} y^{\prime }&=\left (x +y+2\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.559
20274	5941	\begin{align*} -a y+y^{\prime }+2 x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.561
20275	18502	\begin{align*} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.561
20276	6411	\begin{align*} 24-48 y x +\left (-12 x^{2}+1\right ) \left (y^{2}+3 y^{\prime }\right )+2 x \left (-4 x^{2}+1\right ) \left (y y^{\prime }+y^{\prime \prime }-y^{3}\right )&=0 \\ \end{align*}	✗	✗	✗	✗	4.562
20277	20218	\begin{align*} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.563
20278	6571	\begin{align*} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.565
20279	24991	\begin{align*} y^{\prime }-\frac {2 y}{t +1}&=\left (t +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.565
20280	25285	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✓	4.565
20281	16272	\begin{align*} x y^{\prime }&=\sqrt {x}+3 y \\ \end{align*}	✓	✓	✓	✓	4.569
20282	16321	\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.569
20283	20976	\begin{align*} y^{\prime }-y+y^{2} {\mathrm e}^{x}+5 \,{\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= \eta \\ \end{align*}	✓	✓	✓	✓	4.569
20284	4781	\begin{align*} x y^{\prime }+\left (-y x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.570
20285	27	\begin{align*} y^{\prime }&=2 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.572
20286	905	\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y&=8 x^{{4}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.572
20287	3679	\begin{align*} y^{\prime }+\frac {7 y}{x}-3 y^{2}&=\frac {3}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.572
20288	2325	\begin{align*} y^{\prime }&=\frac {3 t^{2}+4 t +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.573
20289	5293	\begin{align*} \left (a +x^{2}+y^{2}\right ) y y^{\prime }&=x \left (a -x^{2}-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✗	4.573
20290	17040	\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.573
20291	6982	\begin{align*} y^{\prime }-y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.576
20292	17894	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.576
20293	25709	\begin{align*} x y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	4.578
20294	22073	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.579
20295	1153	\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.581
20296	2960	\begin{align*} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	4.581
20297	4861	\begin{align*} 3 x y^{\prime }&=3 x^{{2}/{3}}+\left (1-3 y\right ) y \\ \end{align*}	✓	✓	✓	✗	4.582
20298	1558	\begin{align*} \left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y&=\left (x -2\right )^{3} \\ \end{align*}	✓	✓	✓	✓	4.583
20299	18109	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+1\right ) \\ \end{align*}	✓	✓	✓	✓	4.583
20300	20309	\begin{align*} {x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	4.583