2.3.175 Problems 17401 to 17500

Table 2.899: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
17401	1181	\begin{align*} y^{\prime }&=t -1-y^{2} \\ \end{align*}	✓	✓	✓	✗	3.091
17402	1189	\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.094
17403	8419	\begin{align*} y^{\prime }&=\frac {x \left (1-x \right )}{y \left (-2+y\right )} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	3.095
17404	8443	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.095
17405	1226	\begin{align*} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\ \end{align*}	✓	✓	✓	✗	3.096
17406	12443	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )}&=0 \\ \end{align*}	✓	✓	✓	✗	3.096
17407	20859	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.096
17408	17890	\begin{align*} y^{\prime }&=a x +b y+c \\ \end{align*}	✓	✓	✓	✓	3.098
17409	17169	\begin{align*} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y&=t \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.099
17410	22948	\begin{align*} \left (x +1\right ) y^{\prime }&=1+y \\ \end{align*}	✓	✓	✓	✓	3.099
17411	5316	\begin{align*} x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	3.101
17412	9519	\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.102
17413	17150	\begin{align*} y^{\prime }+\cot \left (t \right ) y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	3.102
17414	19919	\begin{align*} x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.102
17415	5373	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right )&=0 \\ \end{align*}	✓	✓	✓	✓	3.103
17416	22970	\begin{align*} y^{\prime }&=1+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	3.103
17417	18019	\begin{align*} y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}	✓	✓	✓	✗	3.104
17418	9731	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	3.105
17419	19346	\begin{align*} y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.105
17420	20827	\begin{align*} y&=y^{\prime } x +\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	3.105
17421	711	\begin{align*} y+3 y^{\prime } x&=12 x \\ \end{align*}	✓	✓	✓	✓	3.106
17422	14220	\begin{align*} \theta ^{\prime }&=t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \\ \end{align*}	✓	✓	✓	✓	3.106
17423	26469	\begin{align*} 1+{y^{\prime }}^{2}&=2 y y^{\prime \prime } \\ \end{align*}	✓	✓	✓	✗	3.106
17424	7553	\begin{align*} y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.107
17425	23184	\begin{align*} y \,{\mathrm e}^{y x}+\left (x \,{\mathrm e}^{y x}+1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.107
17426	15540	\begin{align*} y^{\prime }&=x^{3}+y^{3} \\ \end{align*}	✗	✗	✗	✗	3.108
17427	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*}	✓	✓	✓	✗	3.110
17428	1703	\begin{align*} x^{3} y^{4}+x +\left (y^{3} x^{4}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.111
17429	20951	\begin{align*} y^{\prime }&=y \left (-2+y\right ) \left (3+y\right ) \\ \end{align*}	✓	✓	✓	✓	3.111
17430	674	\begin{align*} y y^{\prime }&=x -1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.112
17431	18791	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	3.112
17432	26057	\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	3.112
17433	11634	\begin{align*} \left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y}&=0 \\ \end{align*}	✓	✓	✓	✗	3.113
17434	4406	\begin{align*} y y^{\prime \prime }-y y^{\prime }&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.114
17435	8302	\begin{align*} y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.114
17436	25709	\begin{align*} y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	3.114
17437	24149	\begin{align*} v v^{\prime }&=g \\ v \left (x_{0} \right ) &= v_{0} \\ \end{align*}	✓	✗	✓	✓	3.115
17438	13206	\begin{align*} y^{\prime }&=f \left (\frac {y}{x}\right ) \\ \end{align*}	✓	✓	✓	✓	3.116
17439	13839	\begin{align*} \left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+3 \left (a x +b \right ) y^{\prime }+d y&=0 \\ \end{align*}	✓	✓	✓	✗	3.116
17440	17306	\begin{align*} y&=t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \\ \end{align*}	✓	✓	✓	✗	3.116
17441	19142	\begin{align*} {y^{\prime \prime \prime }}^{2}+x^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	3.118
17442	20919	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.118
17443	4216	\begin{align*} y^{\prime }&=x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	3.119
17444	7036	\begin{align*} 2 y^{3} y^{\prime }+x y^{2}-x^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	3.119
17445	9127	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.119
17446	21006	\begin{align*} x^{\prime }&=-2 x+3 \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.119
17447	8868	\begin{align*} y^{\prime }-2 y&=x^{2}+x \\ \end{align*}	✓	✓	✓	✓	3.120
17448	80	\begin{align*} y+3 y^{\prime } x&=12 x \\ \end{align*}	✓	✓	✓	✓	3.121
17449	794	\begin{align*} 9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	3.122
17450	21995	\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.122
17451	25905	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \\ \end{align*}	✓	✓	✓	✓	3.124
17452	1705	\begin{align*} x^{3} y^{4}+2 x +\left (y^{3} x^{4}+3 y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.126
17453	12644	\begin{align*} y^{\prime \prime }&=-\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \\ \end{align*}	✓	✓	✓	✗	3.126
17454	24984	\begin{align*} y^{\prime }&=-\frac {y}{t}+\cos \left (t^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	3.126
17455	15892	\begin{align*} y^{\prime }&=y-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.127
17456	8389	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	3.128
17457	16270	\begin{align*} y^{\prime } x +3 y-10 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	3.128
17458	17638	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.128
17459	17160	\begin{align*} x^{\prime }&=\frac {3 x t^{2}}{-t^{3}+1} \\ \end{align*}	✓	✓	✓	✓	3.129
17460	4626	\begin{align*} y^{\prime }&=1-\cot \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	3.130
17461	15542	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	3.131
17462	33	\begin{align*} y y^{\prime }&=x -1 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.132
17463	15369	\begin{align*} y^{\prime }-\frac {n y}{x}&={\mathrm e}^{x} x^{n} \\ \end{align*}	✓	✓	✓	✓	3.132
17464	7602	\begin{align*} 3 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.134
17465	22073	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.134
17466	6869	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-\frac {2 a}{3}} \\ \end{align*}	✓	✓	✓	✗	3.135
17467	14253	\begin{align*} \left (t^{2}+1\right ) x^{\prime }&=-3 t x+6 t \\ \end{align*}	✓	✓	✓	✓	3.135
17468	6048	\begin{align*} a y-2 x^{2} \tan \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.136
17469	17015	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.136
17470	3976	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.137
17471	8450	\begin{align*} y^{\prime } x +y&=4 x +1 \\ y \left (1\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.138
17472	19682	\begin{align*} t x^{\prime }+x \ln \left (t \right )&=t^{2} \\ \end{align*}	✓	✓	✓	✓	3.138
17473	22584	\begin{align*} 2 x^{2}-{\mathrm e}^{x} y-{\mathrm e}^{x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.138
17474	9737	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	3.139
17475	11444	\begin{align*} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	3.139
17476	1219	\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \\ \end{align*}	✓	✓	✓	✓	3.140
17477	3325	\begin{align*} y&=y^{\prime } x +\frac {1}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	3.140
17478	6490	\begin{align*} 4 y y^{\prime \prime }&=a y+b y^{2}+c y^{3}+3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.140
17479	7974	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✓	3.141
17480	12426	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +a y&=0 \\ \end{align*}	✓	✓	✓	✓	3.141
17481	14433	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}	✓	✗	✗	✗	3.141
17482	22001	\begin{align*} x^{2}+1+\left (y^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.141
17483	18619	\begin{align*} y^{\prime } x +\left (x +1\right ) y&=x \\ \end{align*}	✓	✓	✓	✓	3.142
17484	1241	\begin{align*} 2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.143
17485	2303	\begin{align*} t^{2} y+y^{\prime }&=t^{2} \\ \end{align*}	✓	✓	✓	✓	3.143
17486	25821	\begin{align*} y^{\prime }&={\mathrm e}^{3 x +2 y} \\ \end{align*}	✓	✓	✓	✓	3.144
17487	725	\begin{align*} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	3.145
17488	3316	\begin{align*} 4 x {y^{\prime }}^{2}+2 y^{\prime } x&=y \\ \end{align*}	✓	✓	✓	✓	3.145
17489	15933	\begin{align*} y^{\prime }&=a t y+4 \,{\mathrm e}^{-t^{2}} \\ \end{align*}	✓	✓	✓	✓	3.146
17490	1616	\begin{align*} y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ \end{align*}	✗	✗	✗	✗	3.148
17491	8305	\begin{align*} y^{\prime }&=x \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.148
17492	18513	\begin{align*} \frac {y}{t}+y^{\prime }&=5+\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	3.148
17493	20099	\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \\ \end{align*}	✓	✓	✓	✓	3.148
17494	20734	\begin{align*} \left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\ \end{align*}	✓	✓	✓	✓	3.148
17495	23200	\begin{align*} x^{2}-y^{2}+x +2 y y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.148
17496	1151	\begin{align*} y^{\prime }&=2 y^{2}+x y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.149
17497	8879	\begin{align*} y^{\prime }-\tan \left (x \right ) y&={\mathrm e}^{\sin \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	3.149
17498	9008	\begin{align*} y^{\prime }&=\frac {x^{2}+x}{y-y^{2}} \\ \end{align*}	✓	✓	✓	✓	3.150
17499	10236	\begin{align*} y^{\prime \prime }&=A y^{{2}/{3}} \\ \end{align*}	✓	✓	✓	✓	3.150
17500	19267	\begin{align*} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.150