2.3.192 Problems 19101 to 19200

Table 2.957: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19101	8903	\begin{align*} y^{\prime \prime }+10 y&=0 \\ y \left (0\right ) &= \pi \\ y^{\prime }\left (0\right ) &= \pi ^{2} \\ \end{align*}	✓	✓	✓	✓	3.685
19102	20978	\begin{align*} x y^{2}-y^{3}+\left (1-x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.685
19103	3599	\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\ \end{align*}	✓	✓	✓	✓	3.687
19104	11855	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) \sin \left (x y^{\prime }-y\right )^{2}-1&=0 \\ \end{align*}	✓	✓	✓	✗	3.687
19105	14373	\begin{align*} x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.688
19106	24244	\begin{align*} y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.688
19107	21832	\begin{align*} 1-x y^{\prime }&=\ln \left (y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.689
19108	24187	\begin{align*} 2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.689
19109	3001	\begin{align*} 1+x y \left (1+x y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	3.690
19110	7607	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	3.690
19111	7628	\begin{align*} \sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	3.690
19112	14901	\begin{align*} y^{\prime }+{\mathrm e}^{-x} y&=1 \\ y \left (0\right ) &= {\mathrm e} \\ \end{align*}	✓	✓	✓	✓	3.690
19113	26366	\begin{align*} 2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	3.690
19114	8270	\begin{align*} y^{\prime }&=6 \sqrt {y}+5 x^{3} \\ y \left (-1\right ) &= 4 \\ \end{align*}	✗	✗	✗	✗	3.691
19115	12063	\begin{align*} y^{\prime }&=\frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\ \end{align*}	✓	✓	✓	✗	3.691
19116	17933	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.691
19117	1700	\begin{align*} \left (2 x -1\right ) \left (-1+y\right )+\left (x +2\right ) \left (x -3\right ) y^{\prime }&=0 \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.692
19118	25556	\begin{align*} y^{\prime \prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	3.692
19119	23882	\begin{align*} 3 y^{2}+y \sin \left (2 y x \right )+\left (6 y x +x \sin \left (2 y x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.693
19120	4235	\begin{align*} {\mathrm e}^{y} y^{\prime }+2 x&=2 x \,{\mathrm e}^{y} \\ \end{align*}	✓	✓	✓	✓	3.694
19121	5355	\begin{align*} {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	3.694
19122	17015	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.694
19123	23152	\begin{align*} x y^{\prime }+y&=3 x \\ \end{align*}	✓	✓	✓	✓	3.694
19124	4978	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{3}+y \\ \end{align*}	✓	✓	✓	✓	3.695
19125	6592	\begin{align*} -{y^{\prime }}^{2}+4 y {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.695
19126	128	\begin{align*} 2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.697
19127	20818	\begin{align*} x^{\prime }-2 x&={\mathrm e}^{2 t} t \\ \end{align*}	✓	✓	✓	✓	3.697
19128	24121	\begin{align*} \sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.697
19129	9731	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	3.698
19130	6462	\begin{align*} b {y^{\prime }}^{2}+\left (y+a \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.699
19131	8069	\begin{align*} x y^{\prime }&=1-x +2 y \\ \end{align*}	✓	✓	✓	✓	3.699
19132	146	\begin{align*} \frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.700
19133	195	\begin{align*} {\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.700
19134	711	\begin{align*} 3 x y^{\prime }+y&=12 x \\ \end{align*}	✓	✓	✓	✓	3.700
19135	1543	\begin{align*} x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \\ y \left ({\mathrm e}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.700
19136	12967	\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.700
19137	14007	\begin{align*} \left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\ \end{align*}	✓	✓	✓	✓	3.700
19138	1227	\begin{align*} \frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y}&=0 \\ \end{align*}	✓	✓	✓	✓	3.701
19139	1230	\begin{align*} y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	3.701
19140	17095	\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}	✓	✓	✓	✓	3.701
19141	25573	\begin{align*} a y^{\prime \prime }+b y^{\prime }+c y&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.701
19142	4219	\begin{align*} \left (1-x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	3.702
19143	16240	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.703
19144	5403	\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }&=b c \,x^{2} \\ \end{align*}	✓	✓	✓	✓	3.704
19145	9008	\begin{align*} y^{\prime }&=\frac {x^{2}+x}{y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.704
19146	9580	\begin{align*} y^{\prime \prime }-x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	3.704
19147	23139	\begin{align*} p^{\prime }&=a p-b p^{2} \\ \end{align*}	✓	✓	✓	✓	3.704
19148	27410	\begin{align*} \left (x y^{\prime }+y\right )^{2}&=x^{2} y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.704
19149	11338	\begin{align*} y^{\prime }+y^{3}+a x y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.705
19150	13872	\begin{align*} x^{4} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.706
19151	19675	\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\ \end{align*}	✓	✓	✓	✓	3.706
19152	14905	\begin{align*} x^{\prime }+\left (a +\frac {1}{t}\right ) x&=b \\ x \left (1\right ) &= x_{0} \\ \end{align*}	✓	✓	✓	✗	3.708
19153	16283	\begin{align*} y x +x^{2} y^{\prime }&=\sqrt {x}\, \sin \left (x \right ) \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.708
19154	3051	\begin{align*} 4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.709
19155	6027	\begin{align*} a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&={\mathrm e}^{x} x^{2+a} \\ \end{align*}	✓	✓	✓	✗	3.709
19156	8056	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	3.711
19157	19805	\begin{align*} y \left (y+3\right ) y^{\prime }&=x \left (3+2 y\right ) \\ \end{align*}	✓	✓	✓	✓	3.711
19158	10070	\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.712
19159	17797	\begin{align*} 9 x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= -{\frac {1}{2}} \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.714
19160	25697	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.714
19161	18894	\begin{align*} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.715
19162	26433	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.715
19163	4414	\begin{align*} y+3 y^{2} x^{4}+\left (x +2 x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.716
19164	4730	\begin{align*} y^{\prime }&=a +b \sin \left (A x +B y\right ) \\ \end{align*}	✓	✓	✓	✓	3.717
19165	7162	\begin{align*} \sin \left (x \right ) \cos \left (y\right )&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	3.717
19166	25624	\begin{align*} y^{\prime \prime }+y&=1 \\ \end{align*}	✓	✓	✓	✓	3.717
19167	16342	\begin{align*} 3 y-x^{3}+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.718
19168	25428	\begin{align*} y^{\prime }+4 y&=8 \,{\mathrm e}^{-4 t}+20 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.720
19169	173	\begin{align*} x^{\prime }&=1-x^{2} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	3.721
19170	2655	\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	3.721
19171	4038	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.721
19172	20636	\begin{align*} y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 y \sin \left (x \right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.722
19173	4615	\begin{align*} y^{\prime }&=x \left (x^{2}-y\right ) \\ \end{align*}	✓	✓	✓	✓	3.723
19174	22444	\begin{align*} 3 x^{2}+y+3 x^{3} y+x y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.723
19175	13947	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	3.725
19176	695	\begin{align*} y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.726
19177	4051	\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.727
19178	20141	\begin{align*} a^{2} y^{\prime \prime } y^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	3.727
19179	7339	\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	3.728
19180	21953	\begin{align*} y y^{\prime \prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✗	3.728
19181	5361	\begin{align*} {y^{\prime }}^{2}&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.731
19182	7696	\begin{align*} \left (x +1\right )^{2} y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.731
19183	9823	\begin{align*} x^{6} {y^{\prime }}^{2}&=8 x y^{\prime }+16 y \\ \end{align*}	✓	✓	✓	✓	3.731
19184	27289	\begin{align*} \left (x^{2}-1\right ) y^{\prime } \sin \left (y\right )+2 x \cos \left (y\right )&=-2 x^{3}+2 x \\ \end{align*}	✓	✓	✓	✓	3.731
19185	17055	\begin{align*} 2 y^{\prime }+y t&=\ln \left (t \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.732
19186	6409	\begin{align*} \left (x y^{\prime }-y\right )^{3}+x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.733
19187	19409	\begin{align*} 3 x^{2} {\mathrm e}^{y}-2 x +\left (x^{3} {\mathrm e}^{y}-\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.733
19188	19614	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.733
19189	42	\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.734
19190	22018	\begin{align*} y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\ \end{align*}	✓	✓	✓	✗	3.734
19191	20891	\begin{align*} x y^{\prime \prime }-x y^{\prime }+y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	3.735
19192	24236	\begin{align*} 3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.735
19193	3561	\begin{align*} y^{\prime }&=\frac {y}{2 x} \\ \end{align*}	✓	✓	✓	✓	3.737
19194	7003	\begin{align*} x y^{\prime }+y&=x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.737
19195	7391	\begin{align*} y^{\prime }&=\frac {\sec \left (y\right )^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	3.737
19196	21444	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\ \end{align*}	✓	✓	✓	✓	3.737
19197	2996	\begin{align*} \left (x \tan \left (y\right )^{2}+x \right ) y^{\prime }&=2 x^{2}+\tan \left (y\right ) \\ \end{align*}	✓	✓	✓	✗	3.738
19198	13952	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y&=0 \\ \end{align*}	✗	✗	✓	✗	3.738
19199	4836	\begin{align*} \left (x +1\right ) y^{\prime }&={\mathrm e}^{x} \left (x +1\right )^{n +1}+n y \\ \end{align*}	✓	✓	✓	✓	3.739
19200	19312	\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*}	✓	✓	✓	✓	3.740