2.3.194 Problems 19301 to 19400

Table 2.919: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19301	3388	\begin{align*} y^{\prime \prime } x +3 y^{\prime }-y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.687
19302	8343	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.687
19303	15918	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	2.687
19304	16225	\begin{align*} y^{\prime }&=2 x -1+2 y x -y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.687
19305	17713	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.687
19306	5486	\begin{align*} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	2.688
19307	11698	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.688
19308	13355	\begin{align*} y^{\prime }&=a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b \\ \end{align*}	✓	✗	✗	✗	2.688
19309	17934	\begin{align*} \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=2 x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.688
19310	4648	\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.690
19311	8779	\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.691
19312	11696	\begin{align*} x {y^{\prime }}^{2}-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.691
19313	11785	\begin{align*} \left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.691
19314	23299	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=\sin \left (x \right ) \\ \end{align*}	✗	✓	✗	✗	2.691
19315	5278	\begin{align*} x \left (x y^{2}+1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.692
19316	5749	\begin{align*} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.692
19317	7482	\begin{align*} 2 y^{2}+2 y+4 x^{2}+\left (2 y x +x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.692
19318	19078	\begin{align*} y^{\prime } x -4 y&=\sqrt {y}\, x^{2} \\ \end{align*}	✓	✓	✓	✓	2.692
19319	23130	\begin{align*} y^{\prime } x +y^{2}&=1 \\ y \left (-2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.692
19320	24041	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \\ \end{align*}	✓	✓	✓	✓	2.692
19321	7918	\begin{align*} y^{\prime }-y&=y x \\ \end{align*}	✓	✓	✓	✓	2.694
19322	10070	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.694
19323	16357	\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \\ \end{align*}	✓	✓	✓	✓	2.694
19324	17805	\begin{align*} 10 x^{\prime \prime }+\frac {x}{10}&=0 \\ x \left (0\right ) &= -5 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.694
19325	24265	\begin{align*} y^{\prime }&=4 x -2 y \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.695
19326	5351	\begin{align*} \left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.696
19327	11441	\begin{align*} x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2&=0 \\ \end{align*}	✓	✓	✓	✗	2.696
19328	17968	\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.696
19329	24968	\begin{align*} y+1+\left (y-1\right ) \left (t^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.696
19330	9040	\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.697
19331	9090	\begin{align*} x y^{\prime } y&=y-1 \\ \end{align*}	✓	✓	✓	✓	2.697
19332	9199	\begin{align*} -\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.697
19333	13677	\begin{align*} y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.697
19334	13918	\begin{align*} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-x^{n -1} a n -1\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	2.697
19335	20429	\begin{align*} y&=\frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.697
19336	24374	\begin{align*} 4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.697
19337	16977	\begin{align*} y^{\prime }&=-\frac {2 y}{x}-3 \\ \end{align*}	✓	✓	✓	✓	2.698
19338	11309	\begin{align*} y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{-\sin \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✓	2.700
19339	15789	\begin{align*} v^{\prime }&=t^{2} v-2-2 v+t^{2} \\ \end{align*}	✓	✓	✓	✓	2.700
19340	2499	\begin{align*} 3 t y^{\prime }&=y \cos \left (t \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.701
19341	9926	\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (-x +2\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.701
19342	14890	\begin{align*} y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	2.701
19343	16245	\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.701
19344	17331	\begin{align*} x^{\prime }+\frac {x}{y}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.701
19345	23202	\begin{align*} 5 x -y+3 y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.701
19346	20845	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.702
19347	23865	\begin{align*} 2 y \ln \left (x \right ) \ln \left (y\right )+x \left (\ln \left (x \right )^{2}+\ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.702
19348	7975	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=2 \\ \end{align*}	✓	✓	✓	✗	2.705
19349	8189	\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}	✓	✓	✓	✓	2.705
19350	15344	\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.706
19351	15803	\begin{align*} x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\ x \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.706
19352	126	\begin{align*} x^{2} y^{\prime }+2 y x&=5 y^{4} \\ \end{align*}	✓	✓	✓	✓	2.707
19353	1670	\begin{align*} x y^{\prime } y&=3 x^{6}+6 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.707
19354	2488	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.707
19355	2541	\begin{align*} y^{\prime }&=t y^{3}-y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.707
19356	8211	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.707
19357	23165	\begin{align*} y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \\ \end{align*}	✓	✓	✓	✓	2.707
19358	1190	\begin{align*} y^{\prime }&=-b \sqrt {y}+a y \\ \end{align*}	✓	✓	✓	✓	2.708
19359	7494	\begin{align*} y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.708
19360	19396	\begin{align*} y^{\prime }&=1+3 \tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.708
19361	21047	\begin{align*} x^{\prime }&=t x-t^{3} \\ x \left (0\right ) &= a^{2} \\ \end{align*}	✓	✓	✓	✓	2.709
19362	5315	\begin{align*} x \left (a +y^{3} b x \right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.711
19363	15914	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.711
19364	9941	\begin{align*} y^{\prime \prime } x +y^{\prime } x +\left (x^{4}+1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.712
19365	17470	\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.712
19366	603	\begin{align*} x^{\prime }&=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }&=5 x-y-t^{2} \\ \end{align*}	✓	✓	✓	✓	2.713
19367	1646	\begin{align*} x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	2.713
19368	9946	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.714
19369	16323	\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.714
19370	1155	\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\ \end{align*}	✓	✓	✓	✗	2.715
19371	4791	\begin{align*} y^{\prime } x +\left (a +b \,x^{n} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.715
19372	6420	\begin{align*} y y^{\prime \prime }&=a \\ \end{align*}	✓	✓	✓	✗	2.715
19373	14162	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.715
19374	18578	\begin{align*} \ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.716
19375	1694	\begin{align*} x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.717
19376	14438	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.717
19377	20282	\begin{align*} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \\ \end{align*}	✓	✓	✓	✗	2.717
19378	14455	\begin{align*} y^{2}+2 y x -x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.719
19379	20418	\begin{align*} y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	2.719
19380	18067	\begin{align*} x^{2} y^{n} y^{\prime }&=2 y^{\prime } x -y \\ \end{align*}	✓	✓	✓	✗	2.720
19381	3387	\begin{align*} y^{\prime \prime } x +3 y^{\prime }-y&=x \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.721
19382	5701	\begin{align*} \ln \left (y^{\prime }\right )+y^{\prime } x +a&=y \\ \end{align*}	✓	✓	✓	✓	2.721
19383	6350	\begin{align*} a {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.721
19384	8460	\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y&=4 x \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	2.721
19385	11517	\begin{align*} 2 y^{\prime } y-x y^{2}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.721
19386	18517	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.721
19387	19849	\begin{align*} e y^{\prime \prime }&=-\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \\ \end{align*}	✓	✓	✓	✓	2.721
19388	697	\begin{align*} y^{\prime }&=4 x^{3} y-y \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.722
19389	19344	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.722
19390	10068	\begin{align*} y^{\prime }&=2 \sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.723
19391	9933	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.724
19392	22418	\begin{align*} y^{\prime }&=\frac {y \left (-{\mathrm e}^{x}+y\right )}{{\mathrm e}^{x}-2 y x} \\ \end{align*}	✓	✓	✓	✗	2.724
19393	17578	\begin{align*} 2 y y^{\prime \prime }+y^{2}&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.725
19394	22090	\begin{align*} y^{\prime }-\frac {2 y}{x}&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.725
19395	3041	\begin{align*} x \,{\mathrm e}^{-y^{2}}+y^{\prime } y&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.726
19396	9098	\begin{align*} \frac {y^{\prime \prime }}{y^{\prime }}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.727
19397	10370	\begin{align*} {y^{\prime \prime }}^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.727
19398	13068	\begin{align*} x^{\prime }&=a_{1} x+b_{1} y+c_{1} \\ y^{\prime }&=a_{2} x+b_{2} y+c_{2} \\ \end{align*}	✓	✓	✓	✓	2.727
19399	17084	\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.729
19400	24286	\begin{align*} x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.729