2.3.192 Problems 19101 to 19200

Table 2.915: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
19101	15946	\begin{align*} y^{\prime }&=t y \\ \end{align*}	✓	✓	✓	✓	2.580
19102	21450	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.580
19103	9387	\begin{align*} \left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.581
19104	14838	\begin{align*} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \\ \end{align*}	✗	✓	✗	✗	2.581
19105	5864	\begin{align*} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.582
19106	3552	\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \\ \end{align*}	✓	✓	✓	✓	2.583
19107	15546	\begin{align*} y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	2.585
19108	15795	\begin{align*} x^{\prime }&=-t x \\ x \left (0\right ) &= \frac {1}{\sqrt {\pi }} \\ \end{align*}	✓	✓	✓	✓	2.585
19109	20891	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&={\mathrm e}^{x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✗	✓	✓	✗	2.585
19110	4843	\begin{align*} \left (x +a \right ) y^{\prime }+b \,x^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.586
19111	22381	\begin{align*} y^{\prime } x&=2 x +3 y \\ \end{align*}	✓	✓	✓	✓	2.586
19112	24362	\begin{align*} 2 x -3 y+4+3 \left (x -1\right ) y^{\prime }&=0 \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.586
19113	5842	\begin{align*} b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.587
19114	13689	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.587
19115	22555	\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}	✓	✓	✓	✓	2.587
19116	4614	\begin{align*} y^{\prime }&=a +b \,{\mathrm e}^{k x}+c y \\ \end{align*}	✓	✓	✓	✓	2.588
19117	7536	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.588
19118	12500	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	2.588
19119	15774	\begin{align*} y^{\prime }&=\frac {1+y}{t +1} \\ \end{align*}	✓	✓	✓	✓	2.588
19120	7941	\begin{align*} y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.589
19121	8859	\begin{align*} y^{\prime }+y \cos \left (x \right )&=\cos \left (x \right ) \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.589
19122	11469	\begin{align*} x^{3} y^{\prime }-y^{2}-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✓	2.589
19123	12362	\begin{align*} y^{\prime \prime } x +y^{\prime }+\left (x +a \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.589
19124	65	\begin{align*} -y+y^{\prime } x&=2 x^{2} y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.590
19125	7001	\begin{align*} y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.590
19126	12104	\begin{align*} y^{\prime }&=\frac {x \left ({\mathrm e}^{-2 x^{2}} x^{4}-4 x^{2} {\mathrm e}^{-x^{2}} y-4 x^{2} {\mathrm e}^{-x^{2}}+4 y^{2}+4 \,{\mathrm e}^{-x^{2}}\right )}{4} \\ \end{align*}	✓	✓	✓	✓	2.590
19127	21479	\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.590
19128	22549	\begin{align*} \left (\sin \left (y\right )-x \right ) y^{\prime }&=2 x +y \\ y \left (1\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✗	2.590
19129	1602	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \\ y \left (\pi \right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.592
19130	17127	\begin{align*} y^{\prime }&=-\frac {y-2}{x -2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.592
19131	1572	\begin{align*} \left (x^{2}-1\right ) y^{\prime }-2 y x&=x \left (x^{2}-1\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.593
19132	5311	\begin{align*} \left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	2.595
19133	19489	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.596
19134	3244	\begin{align*} y^{\prime \prime }&=k^{2} y \\ \end{align*}	✓	✓	✓	✓	2.597
19135	12600	\begin{align*} y^{\prime \prime }&=-\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (x +a \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (x +a \right )^{2} \left (x +b \right )} \\ \end{align*}	✓	✓	✓	✗	2.597
19136	4207	\begin{align*} \sin \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✗	2.598
19137	5341	\begin{align*} x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	2.598
19138	6825	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.598
19139	15956	\begin{align*} y^{\prime }&=3 y+2 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.598
19140	4654	\begin{align*} y^{\prime }+1-x&=y \left (x +y\right ) \\ \end{align*}	✓	✓	✓	✗	2.599
19141	17400	\begin{align*} y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	2.599
19142	9094	\begin{align*} \frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.600
19143	4642	\begin{align*} y^{\prime }&=\sin \left (2 x \right )+\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.601
19144	9154	\begin{align*} x^{2} y^{\prime }&=y^{2}+2 y x \\ \end{align*}	✓	✓	✓	✓	2.602
19145	11417	\begin{align*} y^{\prime } x -y \ln \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.602
19146	14432	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✗	✗	✗	2.602
19147	11396	\begin{align*} y^{\prime } x -y^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	2.603
19148	22023	\begin{align*} x +\sin \left (y\right )+\left (x \cos \left (y\right )-2 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.603
19149	7011	\begin{align*} \left (y^{2}+a \sin \left (x \right )\right ) y^{\prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.605
19150	9945	\begin{align*} y^{\prime \prime } x -\left (2+x \right ) y^{\prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.605
19151	15927	\begin{align*} y^{\prime }&=\sin \left (t \right ) y+4 \\ \end{align*}	✓	✓	✓	✓	2.605
19152	4620	\begin{align*} y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )-y \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.607
19153	9936	\begin{align*} x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.607
19154	3028	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.608
19155	3658	\begin{align*} y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.608
19156	4702	\begin{align*} y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\ \end{align*}	✓	✓	✓	✓	2.608
19157	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*}	✓	✓	✓	✓	2.608
19158	11762	\begin{align*} 4 y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.608
19159	21279	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=\lambda x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✗	✗	✓	✓	2.608
19160	5866	\begin{align*} -a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.611
19161	17846	\begin{align*} y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\ \end{align*}	✓	✓	✓	✓	2.611
19162	3008	\begin{align*} 2 y x -2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 y^{2} x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.612
19163	5426	\begin{align*} {y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.612
19164	7162	\begin{align*} \cos \left (y\right ) \sin \left (x \right )&=\cos \left (x \right ) \sin \left (y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.612
19165	8233	\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.612
19166	18488	\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.612
19167	1599	\begin{align*} \left (x +1\right ) \left (x -2\right ) y^{\prime }+y&=0 \\ y \left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.613
19168	19889	\begin{align*} z^{\prime }+5 y-2 z&=x \\ y^{\prime }+4 y+z&=x \\ \end{align*}	✓	✓	✓	✓	2.614
19169	707	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.615
19170	6828	\begin{align*} \cos \left (y\right ) \sin \left (x \right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.615
19171	8672	\begin{align*} x +2 x^{3}+\left (2 y^{3}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.615
19172	13917	\begin{align*} \left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{-2+n} \left (b \,x^{m +1}+a n -a \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	2.615
19173	22011	\begin{align*} y^{\prime }&=y x \\ y \left (1\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	2.615
19174	3606	\begin{align*} y^{\prime }&=y^{3} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.617
19175	7563	\begin{align*} y^{\prime }-4 y&=2 x y^{2} \\ y \left (0\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	2.618
19176	15818	\begin{align*} y^{\prime }&=\left (t +1\right ) y \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✓	✓	2.618
19177	21617	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.620
19178	12340	\begin{align*} y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.621
19179	19751	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.621
19180	55	\begin{align*} y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\ \end{align*}	✓	✓	✓	✗	2.622
19181	13217	\begin{align*} \left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0}&=0 \\ \end{align*}	✓	✓	✓	✗	2.622
19182	17159	\begin{align*} y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.622
19183	20238	\begin{align*} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.622
19184	7019	\begin{align*} \left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.623
19185	12919	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}-a&=0 \\ \end{align*}	✓	✓	✓	✗	2.623
19186	1536	\begin{align*} y^{\prime }&=-1-\frac {x}{2}+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \\ \end{align*}	✓	✓	✓	✓	2.625
19187	4205	\begin{align*} \cos \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.625
19188	15936	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	2.625
19189	11765	\begin{align*} \left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c&=0 \\ \end{align*}	✓	✓	✓	✓	2.626
19190	22601	\begin{align*} x^{2} y^{3}+2 x y^{2}+y+\left (x^{3} y^{2}-2 x^{2} y+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✗	✓	2.626
19191	11481	\begin{align*} x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.627
19192	4213	\begin{align*} y^{\prime }&=6 x y^{2} \\ \end{align*}	✓	✓	✓	✓	2.628
19193	5058	\begin{align*} \left (x +y\right ) y^{\prime }+\tan \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.628
19194	7709	\begin{align*} x^{3}+\left (1+y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.628
19195	4619	\begin{align*} y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )+y \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.629
19196	8881	\begin{align*} y^{\prime }+y \cos \left (x \right )&={\mathrm e}^{-\sin \left (x \right )} \\ y \left (\pi \right ) &= \pi \\ \end{align*}	✓	✓	✓	✓	2.631
19197	8694	\begin{align*} 2 y^{\prime } x&=\left (2 x^{2}-y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✓	2.632
19198	8873	\begin{align*} L y^{\prime }+R y&=E \sin \left (\omega x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.632
19199	9816	\begin{align*} {y^{\prime }}^{4}+y^{\prime } x -3 y&=0 \\ \end{align*}	✓	✓	✗	✗	2.632
19200	16281	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (3+3 x^{2}-y\right ) \\ y \left (2\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	2.632