2.3.195 Problems 19401 to 19500

Table 2.963: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19401	17148	\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\ \end{align*}	✓	✓	✓	✓	3.884
19402	22485	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.884
19403	19331	\begin{align*} x y^{\prime }-y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.886
19404	4325	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.887
19405	4077	\begin{align*} 2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.888
19406	5296	\begin{align*} 2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\ \end{align*}	✓	✓	✓	✗	3.888
19407	18052	\begin{align*} \left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.888
19408	1822	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	3.891
19409	17305	\begin{align*} y&=t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \\ \end{align*}	✓	✓	✓	✓	3.891
19410	25208	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\ y \left (1\right ) &= -1 \\ y^{\prime }\left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.891
19411	4220	\begin{align*} y^{\prime }&=\frac {4 x y}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.892
19412	6030	\begin{align*} -2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=1+x +2 x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.894
19413	23269	\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.894
19414	24293	\begin{align*} y-\sin \left (x \right )^{2}+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.894
19415	12887	\begin{align*} 9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.895
19416	20279	\begin{align*} y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	3.895
19417	26231	\begin{align*} x^{6}-2 x^{5}+2 x^{4}-y^{3}+4 x^{2} y+\left (x y^{2}-4 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.895
19418	3295	\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	3.897
19419	1186	\begin{align*} y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.898
19420	4338	\begin{align*} y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.899
19421	7467	\begin{align*} {\mathrm e}^{t} y+t \,{\mathrm e}^{t} y+\left ({\mathrm e}^{t} t +2\right ) y^{\prime }&=0 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	3.900
19422	4584	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	3.901
19423	5243	\begin{align*} \left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.901
19424	5889	\begin{align*} x y^{\prime \prime }+y^{\prime }&=x^{n} \\ \end{align*}	✓	✓	✓	✓	3.901
19425	22106	\begin{align*} y^{\prime \prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.901
19426	26216	\begin{align*} \ln \left (y\right ) y+x y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.901
19427	18875	\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=g \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	3.902
19428	19083	\begin{align*} x y^{\prime }+y&=x y^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.902
19429	25795	\begin{align*} y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\ y \left (2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.902
19430	27399	\begin{align*} y&=x y^{\prime }-y^{\prime }-2 \\ \end{align*}	✓	✓	✓	✓	3.902
19431	11803	\begin{align*} \left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.903
19432	21351	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	3.904
19433	2342	\begin{align*} 2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✗	3.905
19434	4635	\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \\ \end{align*}	✓	✓	✓	✗	3.905
19435	16275	\begin{align*} 2 \sqrt {x}\, y^{\prime }+y&=2 x \,{\mathrm e}^{-\sqrt {x}} \\ \end{align*}	✓	✓	✓	✓	3.905
19436	19907	\begin{align*} x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.905
19437	14413	\begin{align*} y^{\prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	3.906
19438	2485	\begin{align*} y t +\left (t^{2}+1\right ) y^{\prime }&=\left (t^{2}+1\right )^{{5}/{2}} \\ \end{align*}	✓	✓	✓	✓	3.907
19439	15020	\begin{align*} x^{\prime }+3 x&={\mathrm e}^{2 t} \\ \end{align*}	✓	✓	✓	✓	3.907
19440	18806	\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.907
19441	17284	\begin{align*} -2 y+y^{\prime }&=t^{2} \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.908
19442	14509	\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.909
19443	23236	\begin{align*} y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{y} \\ \end{align*}	✓	✓	✓	✗	3.909
19444	25206	\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=t^{5} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.909
19445	8831	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.911
19446	18547	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.911
19447	9490	\begin{align*} y^{\prime }-2 y&=x^{2} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.912
19448	21046	\begin{align*} x^{\prime }&=x t -t^{3} \\ x \left (a \right ) &= a^{2} \\ \end{align*}	✓	✓	✓	✓	3.918
19449	26405	\begin{align*} \left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.922
19450	5157	\begin{align*} 2 x y y^{\prime }+1-2 x^{3}-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.927
19451	10226	\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.927
19452	13489	\begin{align*} y^{\prime }&=y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \\ \end{align*}	✓	✓	✓	✗	3.927
19453	16371	\begin{align*} y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.927
19454	66	\begin{align*} y^{\prime }&=2 x y^{2}+3 x^{2} y^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.928
19455	10016	\begin{align*} y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.928
19456	24853	\begin{align*} {y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \\ \end{align*}	✓	✓	✗	✗	3.930
19457	77	\begin{align*} x y^{\prime }+2 y&=3 x \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.931
19458	13954	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	3.931
19459	15176	\begin{align*} \left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.931
19460	21371	\begin{align*} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.931
19461	2492	\begin{align*} \cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.932
19462	17283	\begin{align*} y^{\prime }+2 y&=t^{2} \sqrt {y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.932
19463	24261	\begin{align*} \left (2 x +3\right ) y^{\prime }&=y+\sqrt {2 x +3} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.932
19464	24126	\begin{align*} v^{\prime }&=-\frac {v}{p} \\ \end{align*}	✓	✓	✓	✓	3.933
19465	14144	\begin{align*} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.934
19466	7026	\begin{align*} \cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.935
19467	17236	\begin{align*} -2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.935
19468	11802	\begin{align*} \left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.936
19469	11446	\begin{align*} x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.938
19470	11537	\begin{align*} 2 x y y^{\prime }-y^{2}+a x&=0 \\ \end{align*}	✓	✓	✓	✓	3.938
19471	3463	\begin{align*} y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	3.941
19472	16301	\begin{align*} \left (-x +y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.941
19473	19750	\begin{align*} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align*}	✓	✓	✓	✓	3.942
19474	21599	\begin{align*} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u&=0 \\ u \left (1\right ) &= -1 \\ u^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.942
19475	24980	\begin{align*} \cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.942
19476	2220	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime }&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= -5 \\ \end{align*}	✓	✓	✓	✗	3.943
19477	725	\begin{align*} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.944
19478	1581	\begin{align*} \left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✓	3.944
19479	20983	\begin{align*} y&=x y^{\prime }+a y^{\prime }+b \\ \end{align*}	✓	✓	✓	✓	3.944
19480	23890	\begin{align*} 3 x -2 y+2 y^{2}+\left (2 y x -x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.944
19481	4103	\begin{align*} x y^{\prime }&=x +y \\ y \left (-1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.945
19482	2860	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	3.947
19483	7809	\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.947
19484	4633	\begin{align*} y^{\prime }&=2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	3.948
19485	16279	\begin{align*} x y^{\prime }+3 y&=20 x^{2} \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	3.948
19486	18807	\begin{align*} 2 x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.948
19487	2534	\begin{align*} y^{\prime }&=t \left (1+y\right ) \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.949
19488	25835	\begin{align*} y^{\prime }&=-\frac {2 x y}{x^{2}+1} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.950
19489	8315	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.951
19490	6443	\begin{align*} y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.953
19491	8756	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.953
19492	4236	\begin{align*} y \,{\mathrm e}^{2 x} y^{\prime }+2 x&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.954
19493	6964	\begin{align*} y^{\prime }+a y&=b \\ \end{align*}	✓	✓	✓	✓	3.954
19494	13312	\begin{align*} y^{\prime }&=a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n} \\ \end{align*}	✓	✓	✓	✗	3.957
19495	17949	\begin{align*} x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\ y \left (-\infty \right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	3.957
19496	22558	\begin{align*} y^{\prime }&=3 x +2 y \\ \end{align*}	✓	✓	✓	✓	3.957
19497	5930	\begin{align*} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=4 x^{3} {\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.959
19498	6444	\begin{align*} y y^{\prime \prime }&=g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✗	✓	✓	✗	3.960
19499	8155	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.960
19500	9087	\begin{align*} x y^{\prime }&=\left (-4 x^{2}+1\right ) \tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.961