2.3.188 Problems 18701 to 18800

Table 2.907: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
18701	16311	\begin{align*} y^{\prime } \cos \left (y\right )&={\mathrm e}^{-x}-\sin \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	2.389
18702	14258	\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \\ \end{align*}	✓	✓	✓	✓	2.390
18703	3411	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.391
18704	14498	\begin{align*} x^{\prime }+\frac {\left (t +1\right ) x}{2 t}&=\frac {t +1}{t x} \\ \end{align*}	✓	✓	✓	✓	2.391
18705	4834	\begin{align*} \left (x +1\right ) y^{\prime }&=x^{3} \left (3 x +4\right )+y \\ \end{align*}	✓	✓	✓	✓	2.392
18706	4913	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (2 b x +a \right ) y \\ \end{align*}	✓	✓	✓	✓	2.392
18707	15021	\begin{align*} \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\ \end{align*}	✓	✓	✓	✓	2.393
18708	8029	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=\ln \left (x +1\right )^{2}+x -1 \\ \end{align*}	✓	✓	✓	✗	2.394
18709	20304	\begin{align*} x \left (y^{2}-a^{2}+x^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.394
18710	1559	\begin{align*} y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \\ \end{align*}	✓	✓	✓	✓	2.395
18711	7818	\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.395
18712	198	\begin{align*} y^{\prime } x +3 y&=\frac {3}{x^{{3}/{2}}} \\ \end{align*}	✓	✓	✓	✓	2.396
18713	7505	\begin{align*} y^{\prime }&=\sqrt {x +y}-1 \\ \end{align*}	✓	✓	✓	✓	2.396
18714	21625	\begin{align*} y^{\prime }-k y&=A \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.397
18715	22952	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=1-y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.397
18716	3536	\begin{align*} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.398
18717	18063	\begin{align*} \left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.399
18718	9085	\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.400
18719	15063	\begin{align*} 3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.400
18720	17238	\begin{align*} t^{2} y+t^{3} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.400
18721	18060	\begin{align*} y+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.400
18722	23174	\begin{align*} \left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\ y \left (-1\right ) &= 16 \\ \end{align*}	✓	✓	✓	✓	2.400
18723	18523	\begin{align*} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.402
18724	19230	\begin{align*} y^{\prime }&=k y \\ \end{align*}	✓	✓	✓	✓	2.403
18725	21992	\begin{align*} y^{\prime }&=x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	2.403
18726	15877	\begin{align*} w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \\ \end{align*}	✓	✓	✓	✓	2.404
18727	3442	\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.405
18728	4420	\begin{align*} 2 x^{3} y y^{\prime }+3 y^{2} x^{2}+7&=0 \\ \end{align*}	✓	✓	✓	✓	2.405
18729	14034	\begin{align*} 3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.405
18730	17243	\begin{align*} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.405
18731	5859	\begin{align*} a \csc \left (x \right )^{2} y+\left (2+\cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.406
18732	11567	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.406
18733	21305	\begin{align*} x_{1}^{\prime }&=x_{2}+x_{4} \\ x_{2}^{\prime }&=-x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}+x_{3} \\ x_{4}^{\prime }&=x_{1}-x_{4} \\ \end{align*}	✓	✓	✓	✓	2.406
18734	20796	\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.407
18735	182	\begin{align*} 2 x y^{3}+{\mathrm e}^{x}+\left (3 y^{2} x^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.408
18736	6949	\begin{align*} x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.408
18737	8858	\begin{align*} y^{\prime }+y \cos \left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.408
18738	24278	\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\ \end{align*}	✓	✓	✓	✗	2.409
18739	7792	\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\ \end{align*}	✓	✓	✓	✓	2.410
18740	9534	\begin{align*} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.411
18741	17040	\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.411
18742	22512	\begin{align*} 3-y+2 y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.412
18743	11419	\begin{align*} y^{\prime } x -y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.413
18744	18586	\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.413
18745	22364	\begin{align*} y^{\prime } x&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.413
18746	7564	\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1}-y \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.414
18747	7780	\begin{align*} \frac {x^{\prime \prime }}{2}&=-48 x \\ x \left (0\right ) &= {\frac {1}{6}} \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.414
18748	8510	\begin{align*} y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.414
18749	17216	\begin{align*} {\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.414
18750	12647	\begin{align*} y^{\prime \prime }&=-\frac {\left (-x^{2} \left (a^{2}-1\right )+2 \left (a +3\right ) b x -b^{2}\right ) y}{4 x^{2}} \\ \end{align*}	✗	✓	✓	✗	2.415
18751	18628	\begin{align*} y^{\prime }+y-y^{{1}/{4}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.415
18752	20217	\begin{align*} \left (y x +1\right ) y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.415
18753	27	\begin{align*} y^{\prime }&=2 y^{2} x^{2} \\ y \left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.416
18754	14898	\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.416
18755	1705	\begin{align*} y^{4} x^{3}+2 x +\left (y^{3} x^{4}+3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.417
18756	9203	\begin{align*} \csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✗	✓	2.417
18757	4704	\begin{align*} y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\ \end{align*}	✓	✓	✓	✓	2.418
18758	8179	\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.418
18759	8878	\begin{align*} y^{\prime }+{\mathrm e}^{x} y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.418
18760	18608	\begin{align*} y^{\prime }+\frac {3 y}{t}&=t^{2} y^{2} \\ \end{align*}	✓	✓	✓	✓	2.418
18761	16309	\begin{align*} y^{\prime }&=\left (x -y+3\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.419
18762	12478	\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+f \left (x \right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	2.420
18763	16310	\begin{align*} y^{\prime }+2 x&=2 \sqrt {y+x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.420
18764	4721	\begin{align*} y^{\prime }+\cot \left (x \right ) \cot \left (y\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.421
18765	8455	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right )^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.421
18766	12824	\begin{align*} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✗	2.421
18767	4234	\begin{align*} y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.424
18768	6426	\begin{align*} 2 a^{2} y^{2}+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.424
18769	7349	\begin{align*} \left (x \cos \left (y\right )-{\mathrm e}^{-\sin \left (y\right )}\right ) y^{\prime }+1&=0 \\ \end{align*}	✓	✓	✓	✓	2.424
18770	5227	\begin{align*} \left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.425
18771	18047	\begin{align*} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.426
18772	24367	\begin{align*} y \left (1+2 x -y\right )+x \left (3 x -4 y+3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.426
18773	13653	\begin{align*} x^{2} y^{\prime }&=y^{3}-3 a^{2} x^{4} y+2 a^{3} x^{6}+2 a \,x^{3} \\ \end{align*}	✗	✓	✓	✗	2.427
18774	19979	\begin{align*} x {y^{\prime }}^{2}-2 y^{\prime } y+a x&=0 \\ \end{align*}	✓	✓	✗	✓	2.427
18775	25729	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✗	✗	✗	✗	2.427
18776	5506	\begin{align*} x^{2} {y^{\prime }}^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.428
18777	11491	\begin{align*} y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \\ \end{align*}	✓	✓	✓	✓	2.428
18778	25792	\begin{align*} y^{\prime }&=\frac {x^{2}}{5}+y \\ y \left (2\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.428
18779	1163	\begin{align*} x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.429
18780	14972	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x&=0 \\ x \left (1\right ) &= -1 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.430
18781	4621	\begin{align*} y^{\prime }&={\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.431
18782	7161	\begin{align*} y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\ \end{align*}	✓	✓	✓	✓	2.431
18783	8447	\begin{align*} y^{\prime } y-x&=2 y^{2} \\ y \left (1\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.431
18784	11821	\begin{align*} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.431
18785	23211	\begin{align*} y x +1+y^{2} y^{\prime }&=0 \\ \end{align*}	✗	✗	✗	✗	2.432
18786	1721	\begin{align*} x^{2} y+4 y x +2 y+\left (x^{2}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.434
18787	2968	\begin{align*} x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.434
18788	3644	\begin{align*} 2 x y^{\prime } y-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.434
18789	15552	\begin{align*} y^{\prime }&=\frac {x}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.434
18790	15922	\begin{align*} y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \\ y \left (1\right ) &= 10 \\ \end{align*}	✓	✓	✓	✓	2.434
18791	17120	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.434
18792	13296	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x} \\ \end{align*}	✓	✓	✓	✗	2.435
18793	11459	\begin{align*} \left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.437
18794	15929	\begin{align*} y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.437
18795	8439	\begin{align*} \left (2+x \right )^{2} y^{\prime }&=5-8 y-4 y x \\ \end{align*}	✓	✓	✓	✓	2.438
18796	8506	\begin{align*} x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.438
18797	20234	\begin{align*} \left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=\left (1+y\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.439
18798	20757	\begin{align*} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\ \end{align*}	✓	✓	✓	✗	2.439
18799	24209	\begin{align*} x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.439
18800	25683	\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}	✓	✓	✓	✓	2.439