2.3.195 Problems 19401 to 19500

Table 2.939: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19401	9004	\begin{align*} x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.376
19402	18355	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y \left (2 \pi \right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.376
19403	20291	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.378
19404	21041	\begin{align*} x^{\prime }&=\sin \left (t x\right ) \\ \end{align*}	✗	✗	✗	✗	4.378
19405	17126	\begin{align*} y^{\prime }+y f \left (t \right )&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.379
19406	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*}	✓	✓	✓	✗	4.379
19407	21019	\begin{align*} x^{\prime }+a x&=b t \\ x \left (t_{0} \right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✓	4.379
19408	18595	\begin{align*} \left (1+y^{4}\right ) y^{\prime }&=x^{4}+1 \\ \end{align*}	✓	✓	✓	✓	4.381
19409	5539	\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}	✓	✓	✓	✗	4.382
19410	5993	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.382
19411	20169	\begin{align*} y^{3} y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✓	4.382
19412	1580	\begin{align*} y^{\prime } x +y^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.383
19413	1721	\begin{align*} x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.384
19414	7808	\begin{align*} t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N&=t \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	4.384
19415	16316	\begin{align*} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.384
19416	20971	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\cos \left (y\right )^{2}} \\ y \left (\pi \right ) &= \frac {\pi }{4} \\ \end{align*}	✓	✓	✓	✓	4.385
19417	15918	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	4.388
19418	22564	\begin{align*} s^{\prime }&=\frac {1}{s+t +1} \\ \end{align*}	✓	✓	✓	✓	4.388
19419	6125	\begin{align*} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	4.389
19420	15812	\begin{align*} y^{\prime }&=4 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.389
19421	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*}	✓	✓	✓	✓	4.391
19422	6999	\begin{align*} y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.392
19423	7359	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}+4&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.392
19424	18798	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.392
19425	24320	\begin{align*} y^{\prime }&=\sin \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✓	4.394
19426	13669	\begin{align*} y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.397
19427	5907	\begin{align*} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	4.398
19428	20230	\begin{align*} x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.398
19429	22512	\begin{align*} 3-y+2 y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.398
19430	2990	\begin{align*} y^{\prime }-y x&=\frac {x}{y} \\ \end{align*}	✓	✓	✓	✓	4.399
19431	20830	\begin{align*} y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.401
19432	1245	\begin{align*} 3 t +2 y&=-y^{\prime } t \\ \end{align*}	✓	✓	✓	✓	4.402
19433	2857	\begin{align*} y&=y x +x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	4.403
19434	13757	\begin{align*} y^{\prime \prime } x +\left (x^{n} a +b \right ) y^{\prime }+a \left (b +n -1\right ) x^{n -1} y&=0 \\ \end{align*}	✓	✓	✓	✗	4.404
19435	24251	\begin{align*} 2 x \left (-x^{2}+y\right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.404
19436	26160	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.405
19437	5505	\begin{align*} x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.407
19438	7937	\begin{align*} x^{2} y^{\prime } \cos \left (y\right )&=2 x \sin \left (y\right )-1 \\ \end{align*}	✓	✓	✓	✗	4.409
19439	9199	\begin{align*} -\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.409
19440	22521	\begin{align*} \left (3-x^{2} y\right ) y^{\prime }&=x y^{2}+4 \\ \end{align*}	✓	✓	✓	✗	4.409
19441	714	\begin{align*} y^{\prime } x +y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.410
19442	12307	\begin{align*} y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.410
19443	24271	\begin{align*} x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.411
19444	26080	\begin{align*} {\mathrm e}^{3 y} \sin \left (x \right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.411
19445	2306	\begin{align*} \sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.412
19446	17127	\begin{align*} y^{\prime }&=-\frac {-2+y}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.414
19447	23899	\begin{align*} 3 x^{2} y \ln \left (y\right )+\left (2 x^{3}+2 y^{3}+3 y^{3} \ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.414
19448	4776	\begin{align*} y^{\prime } x&=a \,x^{2}+y+b y^{2} \\ \end{align*}	✓	✓	✓	✗	4.415
19449	6431	\begin{align*} y y^{\prime \prime }&=\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.416
19450	23910	\begin{align*} y^{\prime }+\frac {y}{x}&=\ln \left (x \right )-2 \\ \end{align*}	✓	✓	✓	✓	4.417
19451	15830	\begin{align*} y^{\prime }&=t +t y \\ \end{align*}	✓	✓	✓	✓	4.418
19452	21730	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 7 \\ \end{align*}	✓	✓	✓	✓	4.419
19453	15910	\begin{align*} y^{\prime }+2 y&=3 t^{2}+2 t -1 \\ \end{align*}	✓	✓	✓	✓	4.421
19454	2936	\begin{align*} y^{\prime } x +\ln \left (x \right )-y&=0 \\ \end{align*}	✓	✓	✓	✓	4.422
19455	17908	\begin{align*} y^{\prime }&=2 x \left (\pi +y\right ) \\ \end{align*}	✓	✓	✓	✓	4.422
19456	6928	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.423
19457	16977	\begin{align*} y^{\prime }&=-\frac {2 y}{x}-3 \\ \end{align*}	✓	✓	✓	✓	4.427
19458	53	\begin{align*} y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.428
19459	5027	\begin{align*} y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.429
19460	22051	\begin{align*} 2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.430
19461	14000	\begin{align*} x^{2} y^{\prime }+y^{2}-y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.431
19462	4728	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	4.432
19463	15780	\begin{align*} x^{\prime }&=x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	4.432
19464	4203	\begin{align*} \tan \left (x \right ) y^{\prime }&=y-\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.433
19465	5284	\begin{align*} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.433
19466	11410	\begin{align*} y^{\prime } x +f \left (x \right ) \left (y^{2}-x^{2}\right )-y&=0 \\ \end{align*}	✓	✓	✓	✗	4.433
19467	22596	\begin{align*} y^{\prime }&=\frac {2}{x +2 y-3} \\ \end{align*}	✓	✓	✓	✓	4.434
19468	1690	\begin{align*} \frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.435
19469	5046	\begin{align*} y y^{\prime }&=\csc \left (x \right )^{2}-\cot \left (x \right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	4.435
19470	7442	\begin{align*} 2 y+y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.435
19471	20818	\begin{align*} x^{\prime }-2 x&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	4.435
19472	26164	\begin{align*} x -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.435
19473	26285	\begin{align*} y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	4.438
19474	26278	\begin{align*} 2 y+y^{\prime }&=x^{2}+2 x \\ \end{align*}	✓	✓	✓	✓	4.440
19475	3463	\begin{align*} y^{\prime }-\cot \left (x \right ) y+\frac {1}{\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	4.441
19476	7748	\begin{align*} y^{\prime }+x +x y^{2}&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	4.441
19477	5917	\begin{align*} b y+\left (a +x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	4.445
19478	5744	\begin{align*} \left (x^{2}+a \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.446
19479	6841	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.447
19480	19765	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}	✓	✓	✓	✓	4.447
19481	25783	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.447
19482	2845	\begin{align*} x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.448
19483	5351	\begin{align*} \left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	4.448
19484	18494	\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\ y \left (0\right ) &= -2^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	4.448
19485	13957	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +{\mathrm e}^{\mu x} b \mu \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	4.449
19486	3514	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.450
19487	12879	\begin{align*} y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	4.450
19488	14440	\begin{align*} y^{2}+3+\left (2 y x -4\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.450
19489	20297	\begin{align*} \frac {\left (x +y-a \right ) y^{\prime }}{x +y-b}&=\frac {x +y+a}{x +y+b} \\ \end{align*}	✓	✓	✓	✓	4.450
19490	25490	\begin{align*} y^{\prime }&=a \left (t \right ) y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.450
19491	17121	\begin{align*} y^{\prime }&={\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.451
19492	25011	\begin{align*} -y+y^{\prime }&=t y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.451
19493	5078	\begin{align*} 2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	4.452
19494	4392	\begin{align*} y \left (y-2 y^{\prime } x \right )^{3}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.453
19495	8675	\begin{align*} 2 x \sqrt {1-y^{2}}+y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.453
19496	20812	\begin{align*} y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.453
19497	6978	\begin{align*} -y+y^{\prime } x&=x^{2} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.454
19498	8417	\begin{align*} \left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	4.454
19499	3317	\begin{align*} y&=y^{\prime } x \left (1+y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	4.455
19500	11756	\begin{align*} y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\ \end{align*}	✓	✓	✓	✓	4.458