2.3.162 Problems 16101 to 16200

Table 2.867: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16101	15347	\begin{align*} x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.309
16102	18547	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.310
16103	6868	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-2 a} \\ \end{align*}	✓	✓	✓	✗	2.311
16104	7602	\begin{align*} 3 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.311
16105	3517	\begin{align*} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \\ \end{align*}	✓	✓	✓	✓	2.312
16106	18300	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=x \left (6-\ln \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	2.313
16107	16552	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.314
16108	23279	\begin{align*} \left (x -a \right ) \left (-b +x \right ) y^{\prime \prime }+2 \left (2 x -a -b \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.314
16109	15904	\begin{align*} y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \\ \end{align*}	✓	✓	✓	✓	2.315
16110	24982	\begin{align*} y^{\prime } t +y&={\mathrm e}^{t} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.316
16111	1569	\begin{align*} y^{\prime }+2 y x&=x \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.318
16112	8179	\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.318
16113	15336	\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.318
16114	17621	\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.318
16115	16142	\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.319
16116	25785	\begin{align*} y^{\prime }&=x +y \\ y \left (-2\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.319
16117	16965	\begin{align*} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.320
16118	13667	\begin{align*} y^{\prime \prime }-\left (a \,x^{2}+b x c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.321
16119	15666	\begin{align*} y^{\prime \prime }-4 y&=31 \\ y \left (0\right ) &= -9 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	2.322
16120	21068	\begin{align*} a \,x^{p}+b y+\left (b x +d y^{q}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.322
16121	23100	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.322
16122	24964	\begin{align*} y^{\prime }&=4 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.322
16123	25850	\begin{align*} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.322
16124	14836	\begin{align*} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x&=0 \\ \end{align*}	✓	✓	✓	✗	2.323
16125	18564	\begin{align*} y^{\prime }&=y \left (3-t y\right ) \\ \end{align*}	✓	✓	✓	✓	2.323
16126	22820	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.324
16127	721	\begin{align*} y^{\prime } x&=2 y+x^{3} \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.325
16128	15563	\begin{align*} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.325
16129	3540	\begin{align*} y^{\prime }-\frac {y}{x}&=2 \ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.326
16130	4279	\begin{align*} y^{\prime } x +y&=\cos \left (x \right ) x \\ \end{align*}	✓	✓	✓	✓	2.328
16131	17663	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.328
16132	22765	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x^{2}-4 x +2 \\ \end{align*}	✓	✓	✓	✓	2.328
16133	80	\begin{align*} y+3 y^{\prime } x&=12 x \\ \end{align*}	✓	✓	✓	✓	2.329
16134	3604	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}	✓	✓	✓	✓	2.329
16135	9718	\begin{align*} \left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.329
16136	19406	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.329
16137	20183	\begin{align*} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.329
16138	14988	\begin{align*} x^{\prime }&=2 x+5 y \\ y^{\prime }&=-2 x+\cos \left (3 t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.330
16139	24486	\begin{align*} x^{\prime \prime }+k^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= v_{0} \\ \end{align*}	✓	✓	✓	✓	2.330
16140	25612	\begin{align*} y^{\prime }-a y&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.330
16141	14326	\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.331
16142	15603	\begin{align*} -y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.332
16143	20074	\begin{align*} y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	2.332
16144	6555	\begin{align*} \left (x +y\right ) \left (-y+y^{\prime } x \right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.333
16145	12966	\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.333
16146	14745	\begin{align*} \left (x^{2}-3 x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.333
16147	19330	\begin{align*} y^{\prime } x&=y+x^{2}+9 y^{2} \\ \end{align*}	✓	✓	✓	✓	2.333
16148	12967	\begin{align*} 4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\ \end{align*}	✓	✓	✓	✗	2.334
16149	21334	\begin{align*} -y+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.334
16150	2565	\begin{align*} t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.335
16151	19151	\begin{align*} n \,x^{3} y^{\prime \prime }&=\left (-y^{\prime } x +y\right )^{2} \\ \end{align*}	✗	✓	✓	✗	2.335
16152	1114	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.336
16153	11618	\begin{align*} \left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.336
16154	16264	\begin{align*} y^{\prime }+4 y&=y^{3} \\ \end{align*}	✓	✓	✓	✓	2.336
16155	689	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	2.337
16156	1202	\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.337
16157	4412	\begin{align*} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.337
16158	20482	\begin{align*} -y^{\prime } x +y&=b \left (1+x^{2} y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.338
16159	14838	\begin{align*} \sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \\ \end{align*}	✗	✓	✗	✗	2.339
16160	5047	\begin{align*} y y^{\prime }&=\sqrt {y^{2}+a^{2}} \\ \end{align*}	✓	✓	✓	✓	2.340
16161	9752	\begin{align*} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	2.340
16162	3531	\begin{align*} y^{\prime }+2 y x&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.341
16163	17664	\begin{align*} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.342
16164	1683	\begin{align*} 2 x -2 y^{2}+\left (12 y^{2}-4 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.343
16165	4656	\begin{align*} y^{\prime }&=\left (x -y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.343
16166	8986	\begin{align*} y^{\prime \prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.343
16167	18510	\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-2 t}+t \\ \end{align*}	✓	✓	✓	✓	2.344
16168	14862	\begin{align*} x^{\prime }&=a x+b y \\ y^{\prime }&=c x+d y \\ \end{align*}	✓	✓	✓	✓	2.346
16169	3634	\begin{align*} -y+y^{\prime } x&=\ln \left (x \right ) x^{2} \\ \end{align*}	✓	✓	✓	✓	2.347
16170	17623	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.347
16171	25477	\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.347
16172	25862	\begin{align*} y^{\prime }-2 y&=\cos \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	2.347
16173	5758	\begin{align*} y^{\prime \prime }&=\left (1+2 \tan \left (x \right )^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	2.348
16174	16731	\begin{align*} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.348
16175	25289	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.348
16176	3530	\begin{align*} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.349
16177	3535	\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.349
16178	17158	\begin{align*} y^{\prime }-x&=y \\ \end{align*}	✓	✓	✓	✓	2.349
16179	22318	\begin{align*} y^{\prime }&=2 y x +1 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.349
16180	13204	\begin{align*} g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{0} \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.350
16181	15367	\begin{align*} s^{\prime } \cos \left (t \right )+s \sin \left (t \right )&=1 \\ \end{align*}	✓	✓	✓	✓	2.350
16182	18513	\begin{align*} \frac {y}{t}+y^{\prime }&=5+\cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.350
16183	24952	\begin{align*} y^{\prime } t&=y-2 t y \\ \end{align*}	✓	✓	✓	✓	2.350
16184	3526	\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \\ y \left (0\right ) &= 2 a \\ \end{align*}	✓	✓	✓	✓	2.352
16185	14172	\begin{align*} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.352
16186	18306	\begin{align*} \left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \\ \end{align*}	✓	✓	✓	✗	2.352
16187	12686	\begin{align*} y^{\prime \prime }&=-\frac {a y}{\sin \left (x \right )^{2}} \\ \end{align*}	✗	✓	✓	✗	2.353
16188	18538	\begin{align*} \frac {y}{4}+y^{\prime }&=3+2 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.353
16189	25287	\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.353
16190	25682	\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.355
16191	2634	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.356
16192	18565	\begin{align*} y^{\prime }&=-y \left (3-t y\right ) \\ \end{align*}	✓	✓	✓	✓	2.356
16193	19209	\begin{align*} x^{\prime }&=y \\ y^{\prime }&=z \\ z^{\prime }&=x \\ \end{align*}	✓	✓	✓	✓	2.356
16194	19344	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.356
16195	17187	\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	2.357
16196	3592	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	2.358
16197	7540	\begin{align*} 2 y+y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.358
16198	9344	\begin{align*} y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.359
16199	22356	\begin{align*} y^{\prime \prime }+x {y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	2.359
16200	9055	\begin{align*} y^{\prime } x&=y+x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.360