2.3.162 Problems 16101 to 16200

Table 2.873: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16101	15483	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.405
16102	22223	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.405
16103	23160	\begin{align*} {\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	2.405
16104	23368	\begin{align*} 5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.405
16105	6894	\begin{align*} \frac {-y^{\prime } x +y}{y^{\prime }+y^{2}}&=\frac {-y^{\prime } x +y}{1+x^{2} y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	2.406
16106	25298	\begin{align*} y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.406
16107	5666	\begin{align*} y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.407
16108	14272	\begin{align*} w^{\prime }&=t w+t^{3} w^{3} \\ \end{align*}	✓	✓	✓	✓	2.407
16109	14718	\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.407
16110	17614	\begin{align*} 3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.408
16111	706	\begin{align*} y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	2.410
16112	5211	\begin{align*} \left (x -y^{2}\right ) y^{\prime }&=x^{2}-y \\ \end{align*}	✓	✓	✓	✗	2.410
16113	12654	\begin{align*} y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✗	2.410
16114	17873	\begin{align*} y^{\prime }&=x +y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.410
16115	22453	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.410
16116	21434	\begin{align*} 2 y+y^{\prime }&=1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.411
16117	5696	\begin{align*} {y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right )&=y \\ \end{align*}	✓	✓	✓	✗	2.412
16118	8221	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.412
16119	15558	\begin{align*} y^{\prime }&=4 y-5 \\ y \left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.412
16120	17146	\begin{align*} y^{\prime } x +y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	2.412
16121	22485	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.412
16122	4382	\begin{align*} {y^{\prime }}^{3} x -y {y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.413
16123	16234	\begin{align*} y^{\prime }&=y x -4 x \\ \end{align*}	✓	✓	✓	✓	2.414
16124	20436	\begin{align*} x^{2} \left (-y^{\prime } x +y\right )&=y {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.414
16125	3270	\begin{align*} \left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.415
16126	11434	\begin{align*} x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.415
16127	15844	\begin{align*} y^{\prime }&={\mathrm e}^{\frac {2}{y}} \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✓	2.415
16128	20278	\begin{align*} 1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.415
16129	13764	\begin{align*} y^{\prime \prime } x +\left (x^{n} a +b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y&=0 \\ \end{align*}	✓	✗	✗	✗	2.417
16130	21016	\begin{align*} x^{\prime }&=x+2 t \\ \end{align*}	✓	✓	✓	✓	2.417
16131	2494	\begin{align*} y^{\prime }&=\frac {2 t}{y+t^{2} y} \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.419
16132	160	\begin{align*} y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\ \end{align*}	✓	✓	✓	✓	2.420
16133	203	\begin{align*} 2 y+\left (x +1\right ) y^{\prime }&=3 x +3 \\ \end{align*}	✓	✓	✓	✓	2.420
16134	16269	\begin{align*} y^{\prime }-2 y x&=x \\ \end{align*}	✓	✓	✓	✓	2.420
16135	25893	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{2} \\ \end{align*}	✓	✓	✓	✓	2.420
16136	8875	\begin{align*} y^{\prime }+a y&=b \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.421
16137	20664	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	2.421
16138	8465	\begin{align*} x^{2} y^{\prime }-y&=x^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.422
16139	14490	\begin{align*} y+\left (x y^{2}+x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.422
16140	22484	\begin{align*} y^{\prime } y^{\prime \prime }&=1 \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.422
16141	26193	\begin{align*} y^{\prime }&=x^{2}+2 x -y \\ \end{align*}	✓	✓	✓	✓	2.422
16142	10006	\begin{align*} y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \\ \end{align*}	✓	✓	✓	✓	2.423
16143	20869	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=2 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.423
16144	23972	\begin{align*} y^{\prime }-y x&=-x^{5}+4 x^{3} \\ \end{align*}	✓	✓	✓	✓	2.424
16145	5355	\begin{align*} {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	2.425
16146	9496	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.425
16147	10325	\begin{align*} y^{\prime }&=10+{\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	2.425
16148	5660	\begin{align*} y^{2} {y^{\prime }}^{3}-y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✗	✗	2.426
16149	15815	\begin{align*} y^{\prime }&=3 y \left (1-y\right ) \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	2.427
16150	17529	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y&=2 \ln \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.427
16151	20015	\begin{align*} y&=y^{\prime } x +\frac {m}{y^{\prime }} \\ \end{align*}	✓	✓	✓	✗	2.427
16152	184	\begin{align*} 2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\ \end{align*}	✓	✓	✓	✓	2.428
16153	17613	\begin{align*} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.428
16154	17779	\begin{align*} t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.428
16155	22629	\begin{align*} 4 y^{\prime \prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.429
16156	26056	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	2.430
16157	91	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.431
16158	8581	\begin{align*} y^{\prime \prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.431
16159	19234	\begin{align*} y^{\prime } x&=y+x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.431
16160	26146	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.431
16161	22933	\begin{align*} z+x^{\prime }&=x \\ y^{\prime }-2 x&=y+3 t \\ z^{\prime }+4 y&=z-\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.432
16162	14212	\begin{align*} x^{\prime }&={\mathrm e}^{-2 x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.433
16163	1564	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.434
16164	19297	\begin{align*} y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.434
16165	19344	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.434
16166	19433	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.434
16167	19736	\begin{align*} \theta ^{\prime \prime }&=-p^{2} \theta \\ \end{align*}	✓	✓	✓	✓	2.434
16168	21489	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.435
16169	8444	\begin{align*} y^{\prime }&=x +5 y \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.437
16170	17192	\begin{align*} y^{\prime } t +y&=t \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.437
16171	14970	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.438
16172	17142	\begin{align*} -y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.438
16173	20726	\begin{align*} y-2 y^{\prime } x +a y {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.438
16174	23229	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.438
16175	18836	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.440
16176	22005	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.440
16177	25455	\begin{align*} y^{\prime }&=t^{2}+y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.440
16178	6471	\begin{align*} 2 y y^{\prime \prime }&=4 y^{2}+8 y^{3}+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.441
16179	688	\begin{align*} y y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.442
16180	22603	\begin{align*} y^{\prime }&=\frac {x +y^{2}}{2 y} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.442
16181	15507	\begin{align*} y^{\prime }+y&=x^{2}+2 x -1 \\ \end{align*}	✓	✓	✓	✓	2.443
16182	8435	\begin{align*} y&=\left ({\mathrm e}^{y} y-2 x \right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.444
16183	728	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.445
16184	12582	\begin{align*} -6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.445
16185	10424	\begin{align*} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\ \end{align*}	✗	✓	✓	✗	2.447
16186	16213	\begin{align*} y^{\prime }+y x&=4 x \\ \end{align*}	✓	✓	✓	✓	2.447
16187	18009	\begin{align*} y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\ \end{align*}	✓	✓	✓	✗	2.447
16188	22525	\begin{align*} x^{2}+y^{2}+2 y y^{\prime }&=0 \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.447
16189	22695	\begin{align*} L q^{\prime \prime }+R q^{\prime }+\frac {q}{c}&=E_{0} \sin \left (\omega t \right ) \\ q \left (0\right ) &= 0 \\ q^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.447
16190	25441	\begin{align*} y^{\prime }-a y&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.447
16191	19127	\begin{align*} y^{\prime }&=\sqrt {-x +y} \\ \end{align*}	✓	✓	✓	✓	2.448
16192	22071	\begin{align*} y^{\prime }-\frac {3 y}{x^{2}}&=\frac {1}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	2.448
16193	208	\begin{align*} y^{\prime }&=\sqrt {x +y} \\ \end{align*}	✓	✓	✓	✓	2.449
16194	8446	\begin{align*} y^{\prime } x +y&={\mathrm e}^{x} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.449
16195	4527	\begin{align*} y^{\prime \prime }+4 y&=4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	2.450
16196	5209	\begin{align*} y^{2} y^{\prime }&=x \left (1+y^{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.450
16197	18239	\begin{align*} y^{\prime \prime }+y^{\prime }&=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \\ \end{align*}	✓	✓	✓	✓	2.450
16198	20656	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {a^{2} y}{-x^{2}+1}&=0 \\ \end{align*}	✓	✓	✓	✗	2.450
16199	21018	\begin{align*} x^{\prime }+3 x&=-2 t \\ \end{align*}	✓	✓	✓	✓	2.450
16200	6129	\begin{align*} 2 y-\left (2+x \right ) y^{\prime }+\left (2+x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.451