2.3.271 Problems 27001 to 27100

Table 2.1115: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
27001	5106	\begin{align*} \left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\ \end{align*}	✓	✓	✓	✗	68.718
27002	5117	\begin{align*} \left (a x +b y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✗	68.843
27003	24800	\begin{align*} {y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\ \end{align*}	✓	✓	✓	✗	68.927
27004	5695	\begin{align*} y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right )&=y \\ \end{align*}	✓	✓	✓	✗	69.026
27005	12549	\begin{align*} x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	69.028
27006	19718	\begin{align*} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\ \end{align*}	✓	✓	✓	✗	69.056
27007	6296	\begin{align*} -\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	69.066
27008	19122	\begin{align*} y&={y^{\prime }}^{2} x +{y^{\prime }}^{3} \\ \end{align*}	✓	✓	✓	✗	69.066
27009	26916	\begin{align*} y^{\prime }&=\frac {2 x -5 y-9}{-4 x +y+9} \\ \end{align*}	✓	✓	✓	✓	69.109
27010	5198	\begin{align*} \left (1-x^{3} y\right ) y^{\prime }&=x^{2} y^{2} \\ \end{align*}	✓	✓	✓	✗	69.137
27011	13844	\begin{align*} x^{3} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\ \end{align*}	✗	✓	✓	✗	69.167
27012	12027	\begin{align*} y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \\ \end{align*}	✓	✓	✓	✗	69.211
27013	19909	\begin{align*} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	69.279
27014	7868	\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	69.290
27015	13654	\begin{align*} y^{\prime }&=-\left (a x +b \,x^{m}\right ) y^{3}+y^{2} \\ \end{align*}	✗	✗	✗	✗	69.344
27016	23290	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+y&=2 \\ y \left (\frac {3 \pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {3 \pi }{4}\right ) &= 1 \\ \end{align*}	✗	✗	✗	✗	69.351
27017	18598	\begin{align*} y+\sqrt {x^{2}-y^{2}}&=x y^{\prime } \\ \end{align*}	✓	✓	✓	✓	69.402
27018	22594	\begin{align*} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	69.458
27019	19716	\begin{align*} y^{2}&=x \left (-x +y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	69.461
27020	12558	\begin{align*} 144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \\ \end{align*}	✗	✓	✓	✗	69.462
27021	13431	\begin{align*} y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1} \\ \end{align*}	✓	✗	✗	✗	69.658
27022	25217	\begin{align*} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	69.872
27023	8706	\begin{align*} y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	69.950
27024	7422	\begin{align*} x x^{\prime }+x t^{2}&=\sin \left (t \right ) \\ \end{align*}	✗	✗	✗	✗	69.973
27025	21549	\begin{align*} a_{0} \left (x \right ) y^{\prime \prime }+a_{1} \left (x \right ) y^{\prime }+a_{2} \left (x \right ) y&=f \left (x \right ) \\ \end{align*}	✗	✗	✗	✗	70.091
27026	12532	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	70.312
27027	21453	\begin{align*} 6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	70.533
27028	6196	\begin{align*} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	70.684
27029	5135	\begin{align*} \left (y x +1\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	70.733
27030	5172	\begin{align*} x \left (2 x +3 y\right ) y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	70.752
27031	5515	\begin{align*} {y^{\prime }}^{2} x^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	70.832
27032	17249	\begin{align*} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	70.855
27033	15291	\begin{align*} x^{\prime }&=-3 x-3 y+z \\ y^{\prime }&=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }&=5 x+y+z+39 \,{\mathrm e}^{t} \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 2 \\ z \left (0\right ) &= 3 \\ \end{align*}	✓	✗	✓	✗	70.884
27034	20295	\begin{align*} 2 y+3 x y^{\prime }+2 x y \left (3 y+4 x y^{\prime }\right )&=0 \\ \end{align*}	✓	✓	✓	✗	70.983
27035	17234	\begin{align*} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	71.054
27036	12050	\begin{align*} y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+y x \right )} \\ \end{align*}	✓	✓	✓	✓	71.059
27037	2521	\begin{align*} y^{\prime }&=y^{2}+\cos \left (t \right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	71.095
27038	6259	\begin{align*} -\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	71.174
27039	22790	\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=24 x +24 \\ \end{align*}	✓	✓	✓	✓	71.193
27040	20672	\begin{align*} x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime }+2 y x&=2 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✗	✓	✓	✗	71.210
27041	6197	\begin{align*} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	71.256
27042	24328	\begin{align*} y+x \left (3 y x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	71.441
27043	6167	\begin{align*} -\left (4 p^{2}+1\right ) y-8 x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	71.662
27044	15127	\begin{align*} y y^{\prime }+y^{\prime \prime }&=1 \\ \end{align*}	✗	✓	✓	✗	71.711
27045	12503	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-l y&=0 \\ \end{align*}	✗	✓	✓	✗	71.729
27046	4346	\begin{align*} x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	71.989
27047	11443	\begin{align*} x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c&=0 \\ \end{align*}	✓	✓	✓	✗	72.026
27048	13425	\begin{align*} y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}	✗	✓	✓	✗	72.161
27049	13562	\begin{align*} y y^{\prime }&=a y \cosh \left (x \right )+1 \\ \end{align*}	✗	✗	✗	✗	72.296
27050	12961	\begin{align*} 2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+y^{2} \left (1+a y^{3}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	72.399
27051	20717	\begin{align*} y&=\frac {x}{y^{\prime }}-a y^{\prime } \\ \end{align*}	✓	✓	✓	✗	72.451
27052	13565	\begin{align*} y y^{\prime }&=\left (a x +3 b \right ) y+x^{3} c -a b \,x^{2}-2 b^{2} x \\ \end{align*}	✗	✓	✗	✗	72.455
27053	18043	\begin{align*} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	72.484
27054	20327	\begin{align*} y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \\ \end{align*}	✓	✓	✓	✗	72.490
27055	24162	\begin{align*} v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	72.504
27056	21593	\begin{align*} y^{\prime }&=\frac {x +y+1}{x +2 y+3} \\ \end{align*}	✓	✓	✓	✓	72.520
27057	24311	\begin{align*} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	72.566
27058	204	\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✗	72.585
27059	17909	\begin{align*} x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {11 \pi }{4} \\ \end{align*}	✗	✓	✗	✓	72.735
27060	6835	\begin{align*} 2 x -y+1+\left (-1+2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	72.880
27061	6105	\begin{align*} p \left (1+p \right ) y+\left (1-2 x \right ) y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	72.942
27062	9736	\begin{align*} {y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\ \end{align*}	✓	✓	✓	✗	73.093
27063	24348	\begin{align*} x -4 y-3-\left (x -6 y-5\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	73.102
27064	6147	\begin{align*} 2 a \left (a +1\right ) y-\left (1+3 x \right ) y^{\prime }+2 x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	73.145
27065	12509	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (v -n +1\right ) \left (v +n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	73.158
27066	2934	\begin{align*} \frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )}&=0 \\ \end{align*}	✓	✓	✓	✗	73.228
27067	12533	\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	73.228
27068	14868	\begin{align*} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \\ \end{align*}	✗	✗	✗	✗	73.322
27069	23297	\begin{align*} 2 x y^{\prime \prime }-7 \cos \left (x \right ) y^{\prime }+y&={\mathrm e}^{-x} \\ \end{align*}	✗	✗	✗	✗	73.355
27070	12930	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-\left (a y-1\right ) y^{\prime }+2 y^{2} a^{2}-2 y^{3} b^{2}+a y&=0 \\ \end{align*}	✗	✗	✓	✗	73.522
27071	5429	\begin{align*} {y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	73.582
27072	18339	\begin{align*} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y&=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \\ y \left (\infty \right ) &= 0 \\ \end{align*}	✗	✓	✗	✗	73.719
27073	13554	\begin{align*} y y^{\prime }&=\left (a x +b \right ) y+1 \\ \end{align*}	✗	✓	✓	✗	73.809
27074	5876	\begin{align*} \left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	73.881
27075	6198	\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	74.007
27076	15932	\begin{align*} y^{\prime }&=\frac {y}{\sqrt {t^{3}-3}}+t \\ \end{align*}	✓	✓	✓	✓	74.306
27077	12097	\begin{align*} y^{\prime }&=\frac {\left (y+3\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \\ \end{align*}	✓	✓	✓	✗	74.319
27078	19904	\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	74.422
27079	11798	\begin{align*} \left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	74.567
27080	20121	\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }&=x y^{2} \\ \end{align*}	✗	✗	✗	✗	74.581
27081	6905	\begin{align*} x^{2}+y^{2}&=2 x y y^{\prime } \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	74.717
27082	13922	\begin{align*} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	74.984
27083	24180	\begin{align*} 16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✗	74.984
27084	16191	\begin{align*} y^{\prime }&={\mathrm e}^{-9 x^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	75.109
27085	12508	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (v +n +1\right ) \left (v -n \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	75.222
27086	20450	\begin{align*} \left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✗	75.246
27087	13803	\begin{align*} x^{2} y^{\prime \prime }+x \left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	75.254
27088	6918	\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	75.375
27089	10055	\begin{align*} a y^{2} y^{\prime \prime }+b y^{2}&=c \\ \end{align*}	✓	✓	✓	✗	75.468
27090	5181	\begin{align*} \left (1-x^{2} y\right ) y^{\prime }-1+x y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	75.559
27091	4113	\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	75.641
27092	5948	\begin{align*} y+4 \coth \left (x \right ) y^{\prime }+4 x y^{\prime \prime }&=0 \\ \end{align*}	✗	✗	✗	✗	75.662
27093	14438	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	75.683
27094	11549	\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\ \end{align*}	✗	✗	✗	✗	76.093
27095	16329	\begin{align*} 2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	76.178
27096	12504	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v +1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	76.304
27097	4975	\begin{align*} x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	76.477
27098	11478	\begin{align*} 3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x&=0 \\ \end{align*}	✓	✓	✓	✗	76.540
27099	13999	\begin{align*} 2 x^{3} y-y^{2}-\left (2 x^{4}+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	76.605
27100	2878	\begin{align*} \left (y x -x^{2}\right ) y^{\prime }-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	76.708