2.3.182 Problems 18101 to 18200

Table 2.913: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18101	7361	\begin{align*} y^{\prime } x&=y x +y \\ \end{align*}	✓	✓	✓	✓	3.486
18102	24246	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.486
18103	3028	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.487
18104	19911	\begin{align*} y-y^{\prime } x +\ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.487
18105	15636	\begin{align*} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )} \\ y \left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✗	3.489
18106	16368	\begin{align*} y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.489
18107	11857	\begin{align*} a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\ \end{align*}	✗	✓	✓	✗	3.490
18108	25017	\begin{align*} y y^{\prime }+t y^{2}&=t \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.490
18109	8155	\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.491
18110	20114	\begin{align*} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y&=n^{2} x^{m} \ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.492
18111	4894	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }-1&=y x \\ \end{align*}	✓	✓	✓	✓	3.493
18112	17341	\begin{align*} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	3.493
18113	3567	\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	3.494
18114	8756	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.494
18115	1154	\begin{align*} y^{\prime }&=2 \left (x +1\right ) \left (1+y^{2}\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.496
18116	12824	\begin{align*} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.496
18117	15015	\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.497
18118	17941	\begin{align*} \left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	3.497
18119	19328	\begin{align*} y^{\prime } x&=x^{5}+x^{3} y^{2}+y \\ \end{align*}	✓	✓	✓	✓	3.497
18120	1589	\begin{align*} \left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right )&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.498
18121	6412	\begin{align*} b +a x y-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}	✗	✗	✗	✗	3.498
18122	18030	\begin{align*} \left (y^{\prime } x +y\right )^{2}+3 x^{5} \left (y^{\prime } x -2 y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.499
18123	19959	\begin{align*} y^{\prime } \sqrt {a^{2}+x^{2}}+y&=\sqrt {a^{2}+x^{2}}-x \\ \end{align*}	✓	✓	✓	✓	3.499
18124	20497	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	3.499
18125	24809	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.499
18126	2840	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.500
18127	8823	\begin{align*} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.500
18128	20654	\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \\ \end{align*}	✓	✓	✓	✗	3.501
18129	23728	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.502
18130	1104	\begin{align*} 2 t y+y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.503
18131	4893	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+1&=y x \\ \end{align*}	✓	✓	✓	✓	3.503
18132	19934	\begin{align*} 3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=a \,x^{3} \\ \end{align*}	✓	✓	✓	✓	3.503
18133	24231	\begin{align*} y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.503
18134	5315	\begin{align*} x \left (a +y^{3} b x \right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.504
18135	15021	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\ \end{align*}	✓	✓	✓	✓	3.504
18136	18543	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.504
18137	20600	\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.504
18138	22449	\begin{align*} y^{\prime } x +3 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	3.504
18139	4627	\begin{align*} y^{\prime }&=x \csc \left (x \right )-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.505
18140	5534	\begin{align*} x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	3.505
18141	10151	\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=x \\ \end{align*}	✓	✓	✓	✓	3.505
18142	1522	\begin{align*} 2 y^{\prime }+x \left (-1+y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.506
18143	14248	\begin{align*} x^{\prime }&=-\frac {2 x}{t}+t \\ \end{align*}	✓	✓	✓	✓	3.506
18144	15481	\begin{align*} x^{\prime \prime }&=\left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \\ \end{align*}	✓	✓	✓	✗	3.506
18145	21172	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=t \\ \end{align*}	✓	✓	✓	✓	3.506
18146	4099	\begin{align*} y^{\prime }+y&=x^{2}+2 \\ \end{align*}	✓	✓	✓	✓	3.508
18147	7569	\begin{align*} y^{\prime }+a y&=Q \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.508
18148	7941	\begin{align*} y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.509
18149	26283	\begin{align*} \left (x +1\right ) y^{\prime }-\left (x +1\right )^{4}-2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.509
18150	19805	\begin{align*} y \left (3+y\right ) y^{\prime }&=x \left (3+2 y\right ) \\ \end{align*}	✓	✓	✓	✓	3.510
18151	22560	\begin{align*} r^{\prime }&=\frac {r \left (1+\ln \left (t \right )\right )}{t \left (1+\ln \left (r\right )\right )} \\ \end{align*}	✓	✓	✓	✓	3.510
18152	9743	\begin{align*} x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.511
18153	12527	\begin{align*} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}}&=0 \\ \end{align*}	✓	✓	✓	✗	3.511
18154	24266	\begin{align*} y^{\prime }&=4 x -2 y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.511
18155	2948	\begin{align*} \left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✗	3.512
18156	4640	\begin{align*} y^{\prime }&=\cos \left (x \right )-\tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.512
18157	24965	\begin{align*} y y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	3.512
18158	19726	\begin{align*} p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	3.513
18159	26151	\begin{align*} y^{\prime } x&=y+x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.514
18160	8171	\begin{align*} p^{\prime }&=p \left (1-p\right ) \\ \end{align*}	✓	✓	✓	✓	3.515
18161	5291	\begin{align*} \left (x -x^{2} y-y^{3}\right ) y^{\prime }&=x^{3}-y+x y^{2} \\ \end{align*}	✓	✓	✓	✗	3.516
18162	14429	\begin{align*} y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.516
18163	8506	\begin{align*} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.517
18164	13936	\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	3.517
18165	24986	\begin{align*} y^{\prime }-3 y&=25 \cos \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.517
18166	4629	\begin{align*} y^{\prime }&=\sec \left (x \right )-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.518
18167	19896	\begin{align*} \left (1-x \right ) y^{\prime }-1-y&=0 \\ \end{align*}	✓	✓	✓	✓	3.520
18168	19941	\begin{align*} 3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x^{3}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.520
18169	12922	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	3.521
18170	18522	\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{2 t} t \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.521
18171	4200	\begin{align*} \cot \left (x \right ) y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	3.522
18172	4608	\begin{align*} y^{\prime }&=x +\sin \left (x \right )+y \\ \end{align*}	✓	✓	✓	✓	3.522
18173	6975	\begin{align*} y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	3.522
18174	15359	\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.522
18175	26088	\begin{align*} \left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	3.522
18176	13751	\begin{align*} y^{\prime \prime } x +\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.523
18177	15906	\begin{align*} -2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	3.523
18178	20495	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	3.523
18179	15861	\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \\ y \left (-2\right ) &= -1 \\ \end{align*}	✓	✓	✗	✓	3.525
18180	4896	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+a +y x&=0 \\ \end{align*}	✓	✓	✓	✓	3.530
18181	12077	\begin{align*} y^{\prime }&=\frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (a +x \right )^{3}} \\ \end{align*}	✓	✓	✓	✗	3.531
18182	5091	\begin{align*} \left (x^{3}+2 y\right ) y^{\prime }&=3 x \left (2-y x \right ) \\ \end{align*}	✓	✓	✓	✗	3.532
18183	20137	\begin{align*} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.532
18184	14482	\begin{align*} x^{4} y^{\prime }+2 x^{3} y&=1 \\ \end{align*}	✓	✓	✓	✓	3.533
18185	4526	\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.535
18186	15603	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	3.535
18187	22436	\begin{align*} 2 \sin \left (x \right ) y-\cos \left (x \right )^{3}+\cos \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.535
18188	27	\begin{align*} y^{\prime }&=2 y^{2} x^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.536
18189	4227	\begin{align*} y^{\prime } x&=y x +y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.536
18190	8680	\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}	✓	✓	✓	✓	3.536
18191	24184	\begin{align*} 6 x +y^{2}+y \left (2 x -3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.536
18192	26474	\begin{align*} y^{\prime \prime }&={\mathrm e}^{2 y} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.538
18193	5075	\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	3.539
18194	15354	\begin{align*} t -s+t s^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.540
18195	25858	\begin{align*} 2 \cos \left (x \right ) y-1+\sin \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.540
18196	669	\begin{align*} y^{\prime }&=2 y^{2} x^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.543
18197	1539	\begin{align*} y^{\prime } x +y \ln \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.543
18198	17058	\begin{align*} \left (-2+t \right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	3.543
18199	20109	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \\ \end{align*}	✓	✓	✓	✓	3.543
18200	24477	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.543