2.3.133 Problems 13201 to 13300

Table 2.797: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
13201	21080	\begin{align*} 2 y+x +\left (x^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.381
13202	4293	\begin{align*} {\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-{\mathrm e}^{y} y\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.382
13203	16215	\begin{align*} y^{\prime }&=y x -3 x -2 y+6 \\ \end{align*}	✓	✓	✓	✓	2.382
13204	17	\begin{align*} x^{\prime \prime }&=\frac {1}{\left (1+t \right )^{3}} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.383
13205	15851	\begin{align*} y^{\prime }&=y \left (y-1\right ) \left (y-3\right ) \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✗	✗	2.383
13206	17998	\begin{align*} {y^{\prime }}^{2}-4 y^{\prime } x +2 y+2 x^{2}&=0 \\ \end{align*}	✓	✓	✗	✓	2.383
13207	21953	\begin{align*} y y^{\prime \prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✗	2.383
13208	22402	\begin{align*} y^{\prime }&=\frac {1+\sqrt {x -y}}{1-\sqrt {x -y}} \\ \end{align*}	✓	✓	✓	✓	2.383
13209	24858	\begin{align*} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✗	✗	2.383
13210	2488	\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.384
13211	21399	\begin{align*} y-x y^{2}+y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.384
13212	1564	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.385
13213	8546	\begin{align*} y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.385
13214	12996	\begin{align*} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.385
13215	13931	\begin{align*} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}	✗	✓	✗	✗	2.385
13216	19854	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y&=x \\ \end{align*}	✓	✓	✓	✓	2.385
13217	21512	\begin{align*} y^{\prime }-5 y&={\mathrm e}^{x} x^{3}-x \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	2.387
13218	2630	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.388
13219	6892	\begin{align*} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\ \end{align*}	✓	✓	✓	✓	2.388
13220	9088	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.388
13221	10229	\begin{align*} \frac {x y^{\prime \prime }}{1-x}+y&=\cos \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	2.388
13222	2499	\begin{align*} 3 y^{\prime } t&=y \cos \left (t \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.389
13223	4233	\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.389
13224	5371	\begin{align*} {y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.389
13225	5480	\begin{align*} \left (x +1\right ) {y^{\prime }}^{2}&=y \\ \end{align*}	✓	✓	✓	✓	2.389
13226	19104	\begin{align*} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.389
13227	23383	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ y \left (-1\right ) &= 1 \\ y^{\prime }\left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.389
13228	16360	\begin{align*} y^{2}+1-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.390
13229	20192	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +4 x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.390
13230	3137	\begin{align*} 4 y+y^{\prime \prime }&=12 \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}	✓	✓	✓	✓	2.391
13231	8858	\begin{align*} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.391
13232	13961	\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y&=0 \\ \end{align*}	✓	✓	✗	✗	2.391
13233	22591	\begin{align*} y^{\prime }&=1-\left (x -y\right )^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.391
13234	5990	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.392
13235	7106	\begin{align*} y^{\prime \prime }+y&=4 x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.392
13236	7150	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.392
13237	9882	\begin{align*} 9 x^{2} y^{\prime \prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.392
13238	17321	\begin{align*} y-x +y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.392
13239	4612	\begin{align*} y^{\prime }&=a \cos \left (b x +c \right )+k y \\ \end{align*}	✓	✓	✓	✓	2.393
13240	12922	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}	✓	✓	✓	✗	2.393
13241	18534	\begin{align*} 2 y+y^{\prime } t&=\frac {\sin \left (t \right )}{t} \\ y \left (-\frac {\pi }{2}\right ) &= a \\ \end{align*}	✓	✓	✓	✓	2.393
13242	7388	\begin{align*} x^{\prime }&=\frac {t \,{\mathrm e}^{-t -2 x}}{x} \\ \end{align*}	✓	✓	✓	✓	2.394
13243	12266	\begin{align*} y^{\prime }&=\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+y x}{x^{2}} \\ \end{align*}	✓	✓	✓	✗	2.394
13244	16370	\begin{align*} x +y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.394
13245	13987	\begin{align*} y^{\prime }+\cot \left (x \right ) y&=\sec \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.395
13246	15613	\begin{align*} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	2.395
13247	25753	\begin{align*} y^{\prime }+\sin \left (x \right ) y&=x \\ \end{align*}	✓	✓	✓	✓	2.396
13248	6824	\begin{align*} x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	2.397
13249	16255	\begin{align*} \left (-1+y^{2}\right ) y^{\prime }&=4 y x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.397
13250	4620	\begin{align*} y^{\prime }&=\cos \left (x \right ) \sin \left (x \right )-\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.398
13251	6928	\begin{align*} x -2 y x +{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.398
13252	8220	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (-1\right ) &= 5 \\ y^{\prime }\left (-1\right ) &= -5 \\ \end{align*}	✓	✓	✓	✓	2.398
13253	16726	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.398
13254	5454	\begin{align*} x {y^{\prime }}^{2}+4 y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	2.399
13255	16376	\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \\ \end{align*}	✓	✓	✓	✓	2.399
13256	8525	\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.400
13257	14880	\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.400
13258	8455	\begin{align*} y^{\prime }+\tan \left (x \right ) y&=\cos \left (x \right )^{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	2.401
13259	13237	\begin{align*} y^{\prime } x&=a y^{2}+b y+c \,x^{2 b} \\ \end{align*}	✓	✓	✓	✗	2.401
13260	16380	\begin{align*} x \left (1-2 y\right )+\left (-x^{2}+y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.401
13261	4326	\begin{align*} 2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.402
13262	18525	\begin{align*} \frac {2 y}{t}+y^{\prime }&=\frac {\cos \left (t \right )}{t^{2}} \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.402
13263	25741	\begin{align*} y^{\prime \prime }&=y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.402
13264	10087	\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.403
13265	15336	\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.403
13266	6353	\begin{align*} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.404
13267	21438	\begin{align*} y^{\prime }+\frac {y}{x}&=3 x \\ \end{align*}	✓	✓	✓	✓	2.405
13268	22295	\begin{align*} 2 x +y+\left (x -3\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.405
13269	2657	\begin{align*} t y^{\prime \prime }+y^{\prime } t +2 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	2.406
13270	15563	\begin{align*} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \\ y \left (-1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.406
13271	23102	\begin{align*} y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.406
13272	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
13273	7205	\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}	✓	✓	✓	✓	2.407
13274	97	\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*}	✓	✓	✓	✗	2.408
13275	17036	\begin{align*} y^{\prime }&=y+\frac {1}{1-t} \\ \end{align*}	✓	✓	✓	✓	2.408
13276	23367	\begin{align*} y^{\prime \prime }-2 \left (r +\beta \right ) y^{\prime }+r^{2} y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.408
13277	4414	\begin{align*} y+3 y^{2} x^{4}+\left (x +2 x^{2} y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.410
13278	14722	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=10 x^{2} \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= -6 \\ \end{align*}	✓	✓	✓	✓	2.410
13279	7747	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.412
13280	9764	\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x&=0 \\ y \left (2\right ) &= 5 \\ y^{\prime }\left (2\right ) &= -4 \\ \end{align*}	✓	✓	✓	✓	2.412
13281	6843	\begin{align*} 3 z^{2} z^{\prime }-a z^{3}&=x +1 \\ \end{align*}	✓	✓	✓	✓	2.413
13282	7343	\begin{align*} y^{\prime \prime } x +y^{\prime }&=4 x \\ \end{align*}	✓	✓	✓	✓	2.413
13283	10093	\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.413
13284	5190	\begin{align*} 2 x^{2} y y^{\prime }&=x^{2} \left (2 x +1\right )-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.414
13285	8119	\begin{align*} y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \\ \end{align*} Series expansion around \(x=0\).	✗	✗	✓	✗	2.414
13286	14906	\begin{align*} T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \\ \end{align*}	✓	✓	✓	✓	2.414
13287	7397	\begin{align*} y^{\prime }&=x^{3} \left (1-y\right ) \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.415
13288	12332	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.415
13289	22055	\begin{align*} x^{3} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.415
13290	22634	\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	2.415
13291	25220	\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.415
13292	7514	\begin{align*} y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\ \end{align*}	✓	✓	✓	✓	2.416
13293	8265	\begin{align*} 3 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.416
13294	16120	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.416
13295	16127	\begin{align*} y^{\prime \prime }+9 y&=\cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.416
13296	18547	\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.416
13297	2668	\begin{align*} t y^{\prime \prime }+3 y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	2.418
13298	4609	\begin{align*} y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \\ \end{align*}	✓	✓	✓	✓	2.418
13299	5164	\begin{align*} \left (3-x +2 y x \right ) y^{\prime }+3 x^{2}-y+y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.418
13300	8547	\begin{align*} y^{\prime \prime } x -5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.418