2.3.195 Problems 19401 to 19500

Table 2.933: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19401	7437	\begin{align*} y^{\prime }+\frac {3 y}{x}+2&=3 x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.513
19402	13987	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.513
19403	7711	\begin{align*} x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.515
19404	4410	\begin{align*} {\mathrm e}^{x}+3 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.516
19405	21633	\begin{align*} \left (x -1\right ) y^{\prime \prime }+y^{\prime } x +\frac {y}{x}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.518
19406	2343	\begin{align*} 3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.519
19407	19711	\begin{align*} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.520
19408	25651	\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align*}	✗	✗	✗	✗	4.523
19409	5443	\begin{align*} 4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \\ \end{align*}	✓	✓	✓	✗	4.525
19410	1721	\begin{align*} x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.526
19411	11343	\begin{align*} a y^{3} x +b y^{2}+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.527
19412	9941	\begin{align*} y^{\prime \prime } x +y^{\prime } x +\left (x^{4}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.528
19413	22549	\begin{align*} \left (\sin \left (y\right )-x \right ) y^{\prime }&=2 x +y \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	4.528
19414	5439	\begin{align*} 3 {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	4.529
19415	9143	\begin{align*} 3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.529
19416	14489	\begin{align*} y^{\prime } x +y x +y-1&=0 \\ \end{align*}	✓	✓	✓	✓	4.529
19417	21350	\begin{align*} y^{\prime }&=\frac {x}{y^{3}} \\ \end{align*}	✓	✓	✓	✓	4.529
19418	5977	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.530
19419	22208	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.531
19420	4244	\begin{align*} y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\ \end{align*}	✓	✓	✓	✓	4.533
19421	13008	\begin{align*} x y^{2} y^{\prime \prime }-a&=0 \\ \end{align*}	✗	✓	✓	✗	4.533
19422	11934	\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \\ \end{align*}	✓	✓	✓	✓	4.534
19423	13224	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\ \end{align*}	✓	✓	✓	✗	4.537
19424	22523	\begin{align*} y^{\prime }&=x^{2}+2 y \\ \end{align*}	✓	✓	✓	✓	4.537
19425	4396	\begin{align*} 5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \\ \end{align*}	✓	✓	✗	✓	4.539
19426	8356	\begin{align*} y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\ \end{align*}	✓	✓	✓	✓	4.539
19427	13681	\begin{align*} b y+a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	4.539
19428	4349	\begin{align*} y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	4.542
19429	17955	\begin{align*} \left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \\ \end{align*}	✓	✓	✓	✓	4.542
19430	20962	\begin{align*} y^{\prime }&=\frac {1+y}{2+x}-{\mathrm e}^{\frac {1+y}{2+x}} \\ \end{align*}	✓	✓	✓	✗	4.544
19431	21802	\begin{align*} r^{\prime }&=r \tan \left (t \right ) \\ r \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.544
19432	4723	\begin{align*} y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	4.546
19433	4815	\begin{align*} y^{\prime } x&=\left (-2 x^{2}+1\right ) \cot \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.546
19434	5350	\begin{align*} \left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✗	4.546
19435	14201	\begin{align*} x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\ \end{align*}	✓	✓	✓	✓	4.547
19436	8657	\begin{align*} y^{\prime }&=\frac {x^{2}}{y} \\ \end{align*}	✓	✓	✓	✓	4.548
19437	15781	\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} \\ \end{align*}	✓	✓	✓	✓	4.548
19438	24366	\begin{align*} 2 y \left (x^{2}-y+x \right )+\left (x^{2}-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	4.548
19439	2844	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	4.549
19440	3045	\begin{align*} y^{\prime } x&=x^{4}+4 y \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.549
19441	4937	\begin{align*} x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y&=a \\ \end{align*}	✓	✓	✓	✓	4.549
19442	22550	\begin{align*} n^{\prime }&=-a n \\ n \left (0\right ) &= n_{0} \\ \end{align*}	✓	✓	✓	✓	4.549
19443	2823	\begin{align*} z^{\prime \prime }+z-2 z^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.550
19444	6452	\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	4.554
19445	16225	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	4.554
19446	21819	\begin{align*} y \,{\mathrm e}^{2 x}-3 x \,{\mathrm e}^{2 y}+\left (\frac {{\mathrm e}^{2 x}}{2}-3 x^{2} {\mathrm e}^{2 y}-{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	4.554
19447	19270	\begin{align*} y y^{\prime } x&=\left (x +1\right ) \left (1+y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.555
19448	11585	\begin{align*} \left (b \left (\beta y+x \alpha \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+x \alpha \right )^{2}-\alpha \left (a x +b y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	4.556
19449	23160	\begin{align*} {\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	4.556
19450	2860	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	4.557
19451	4678	\begin{align*} y^{\prime }&=x \left (2+x^{2} y-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	4.557
19452	10091	\begin{align*} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3}&=0 \\ \end{align*}	✗	✓	✓	✗	4.558
19453	20759	\begin{align*} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.559
19454	23908	\begin{align*} y^{\prime }-\frac {2 y}{x}&=-x^{2}+1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.559
19455	25780	\begin{align*} y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.560
19456	16288	\begin{align*} y^{\prime }&=1+\left (-x +y\right )^{2} \\ y \left (0\right ) &= {\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	4.562
19457	5994	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{5} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.563
19458	3673	\begin{align*} y^{\prime }&=\sin \left (3 x -3 y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	4.564
19459	4907	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	4.564
19460	23977	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	4.564
19461	1674	\begin{align*} x \ln \left (x \right )^{2} y^{\prime }&=-4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2} \\ \end{align*}	✓	✓	✓	✗	4.565
19462	8665	\begin{align*} y^{\prime } x +y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	4.565
19463	17251	\begin{align*} -\frac {y}{2}+y^{\prime }&=\frac {t}{y} \\ \end{align*}	✓	✓	✓	✓	4.565
19464	4636	\begin{align*} y^{\prime }&=y \sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.567
19465	2994	\begin{align*} 3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	4.568
19466	15872	\begin{align*} w^{\prime }&=w \cos \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	4.568
19467	8244	\begin{align*} y y^{\prime }&=3 x \\ y \left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	4.569
19468	14504	\begin{align*} x^{\prime }-x&=\sin \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.569
19469	15038	\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ \end{align*}	✓	✓	✓	✗	4.569
19470	15848	\begin{align*} y^{\prime }&=\sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	4.569
19471	17786	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=8 x \\ \end{align*}	✓	✓	✓	✓	4.569
19472	16275	\begin{align*} 2 \sqrt {x}\, y^{\prime }+y&=2 x \,{\mathrm e}^{-\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	4.571
19473	5396	\begin{align*} {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	4.572
19474	4634	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (\sin \left (x \right )^{3}+y\right ) \\ \end{align*}	✓	✓	✓	✗	4.573
19475	19911	\begin{align*} y-y^{\prime } x +\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.574
19476	5329	\begin{align*} x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	4.576
19477	5437	\begin{align*} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\ \end{align*}	✓	✓	✓	✗	4.576
19478	9049	\begin{align*} y^{\prime } x&=2 y \\ \end{align*}	✓	✓	✓	✓	4.580
19479	24978	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{t} \\ y \left (1\right ) &= \sqrt {3} \\ \end{align*}	✓	✓	✓	✓	4.581
19480	6151	\begin{align*} y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	4.582
19481	13674	\begin{align*} y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	4.582
19482	4721	\begin{align*} y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.586
19483	9594	\begin{align*} \left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	4.586
19484	18844	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	4.586
19485	21355	\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\ \end{align*}	✓	✓	✓	✓	4.587
19486	708	\begin{align*} y^{\prime } x +2 y&=3 x \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	4.589
19487	1570	\begin{align*} \left (x -1\right ) y^{\prime }+3 y&=\frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	4.589
19488	4787	\begin{align*} y^{\prime } x +b x +\left (2+a x y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	4.589
19489	11409	\begin{align*} y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	4.589
19490	15749	\begin{align*} y_{1}^{\prime }&=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }&=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	4.590
19491	14388	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-x-14 \\ \end{align*}	✓	✓	✓	✓	4.595
19492	20784	\begin{align*} -y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\ \end{align*}	✓	✓	✓	✗	4.596
19493	24390	\begin{align*} 5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	4.598
19494	11680	\begin{align*} {y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	4.599
19495	18046	\begin{align*} y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	4.599
19496	19301	\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	4.600
19497	24286	\begin{align*} x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✗	4.600
19498	695	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	4.602
19499	9930	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	4.602
19500	14847	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (L \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	4.603