2.3.130 Problems 12901 to 13000

Table 2.791: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
12901	16405	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=2 y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	2.265
12902	4623	\begin{align*} y^{\prime }&={\mathrm e}^{\sin \left (x \right )}-\cos \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.266
12903	10176	\begin{align*} x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.266
12904	20230	\begin{align*} x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.266
12905	20854	\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.266
12906	24308	\begin{align*} y^{\prime }&=3 x +y \\ y \left (-1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.266
12907	83	\begin{align*} y^{\prime } x +y&=3 y x \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.267
12908	3283	\begin{align*} \left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }&={\mathrm e}^{x} y^{\prime } \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.267
12909	8390	\begin{align*} y^{\prime }&=y-y^{3} \\ y \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}	✓	✓	✗	✓	2.267
12910	13344	\begin{align*} y^{\prime }&=y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2} \\ \end{align*}	✓	✓	✓	✗	2.267
12911	15492	\begin{align*} y^{\prime }-y^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	2.267
12912	19455	\begin{align*} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✗	2.267
12913	19747	\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}	✓	✓	✓	✓	2.267
12914	1213	\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.268
12915	21444	\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\ \end{align*}	✓	✓	✓	✓	2.269
12916	8238	\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.270
12917	8654	\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✗	✓	2.270
12918	15967	\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \\ \end{align*}	✓	✓	✓	✓	2.270
12919	21418	\begin{align*} 2 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.270
12920	25700	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align*}	✓	✓	✓	✓	2.270
12921	2510	\begin{align*} 1+{\mathrm e}^{t y} \left (t y+1\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.271
12922	21351	\begin{align*} y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	2.271
12923	8526	\begin{align*} y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.272
12924	23197	\begin{align*} y-2 x -y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.272
12925	1209	\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.273
12926	9777	\begin{align*} y^{\prime \prime }&=x {y^{\prime }}^{2} \\ y \left (2\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\ \end{align*}	✓	✓	✓	✓	2.273
12927	17172	\begin{align*} y^{\prime }&=2 y+{\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.273
12928	20407	\begin{align*} y&=\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.273
12929	13357	\begin{align*} y^{\prime }&=a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b \\ \end{align*}	✓	✓	✓	✗	2.274
12930	4092	\begin{align*} 3 y-2 x +\left (3 x -2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.275
12931	11447	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -1&=0 \\ \end{align*}	✓	✓	✓	✓	2.275
12932	19785	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✓	2.275
12933	19908	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.275
12934	4646	\begin{align*} y^{\prime }&=\csc \left (x \right )+3 \tan \left (x \right ) y \\ \end{align*}	✓	✓	✓	✓	2.276
12935	16490	\begin{align*} y^{\prime \prime }-25 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.276
12936	21454	\begin{align*} y^{\prime }&=\frac {1}{x^{2} y^{3}+y x} \\ \end{align*}	✓	✓	✓	✓	2.276
12937	22514	\begin{align*} s^{2} t s^{\prime }+t^{2}+4&=0 \\ \end{align*}	✓	✓	✓	✓	2.276
12938	5253	\begin{align*} x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (x^{2}+x^{4}+y^{2}\right ) y \\ \end{align*}	✓	✓	✓	✗	2.277
12939	11432	\begin{align*} x^{2} y^{\prime }+y-x&=0 \\ \end{align*}	✓	✓	✓	✓	2.277
12940	12683	\begin{align*} \cos \left (x \right )^{2} y^{\prime \prime }-\left (a \cos \left (x \right )^{2}+n \left (n -1\right )\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	2.277
12941	17193	\begin{align*} y+y^{\prime }&=t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.277
12942	18515	\begin{align*} 2 y+y^{\prime } t&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.277
12943	22534	\begin{align*} \left (x +y\right ) y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.277
12944	24836	\begin{align*} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✗	2.277
12945	15914	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.278
12946	22693	\begin{align*} s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\ s \left (0\right ) &= 0 \\ s^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.278
12947	25000	\begin{align*} y^{\prime } t +3 y&=t^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.278
12948	2319	\begin{align*} y^{\prime }&=1-t +y^{2}-t y^{2} \\ \end{align*}	✓	✓	✓	✓	2.279
12949	6991	\begin{align*} y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.279
12950	16180	\begin{align*} y^{\prime \prime } x +2&=\sqrt {x} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	2.279
12951	19709	\begin{align*} \sqrt {y^{\prime }+y}&=\left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \\ \end{align*}	✗	✗	✗	✗	2.279
12952	19338	\begin{align*} y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.280
12953	771	\begin{align*} x^{3}+3 y-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.281
12954	23128	\begin{align*} -y+y^{\prime } x&=1 \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.281
12955	22450	\begin{align*} y^{2}+y y^{\prime } x&=\left (2 y^{2}+1\right ) y^{\prime } \\ \end{align*}	✓	✓	✓	✓	2.282
12956	4300	\begin{align*} x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.283
12957	8604	\begin{align*} y^{\prime \prime } x +5 y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.283
12958	15924	\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.283
12959	20446	\begin{align*} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }&=3 x y^{2}-x^{2} \\ \end{align*}	✓	✓	✓	✗	2.283
12960	4784	\begin{align*} y^{\prime } x&=a \,x^{3} \left (-y x +1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.284
12961	15372	\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \\ \end{align*}	✓	✓	✓	✓	2.284
12962	19989	\begin{align*} {\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.284
12963	25613	\begin{align*} y^{\prime }-a y&={\mathrm e}^{c t} \\ \end{align*}	✓	✓	✓	✓	2.284
12964	4727	\begin{align*} y^{\prime }&=\cos \left (x \right ) \sec \left (y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.285
12965	17196	\begin{align*} y+y^{\prime }&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.285
12966	837	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.286
12967	4698	\begin{align*} y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\ \end{align*}	✓	✓	✓	✓	2.286
12968	8940	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.286
12969	15650	\begin{align*} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✗	2.286
12970	18185	\begin{align*} y^{\prime \prime }+9 y&=9 \\ \end{align*}	✓	✓	✓	✓	2.286
12971	216	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	2.287
12972	16863	\begin{align*} \sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	2.288
12973	22699	\begin{align*} y^{\prime \prime }+y&=x^{2}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.288
12974	820	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	2.289
12975	8887	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.289
12976	12965	\begin{align*} 3 y y^{\prime \prime }-5 {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	2.289
12977	22154	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (2 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	2.289
12978	24718	\begin{align*} y^{\prime \prime }+2 y^{\prime }&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.289
12979	1101	\begin{align*} \frac {y}{t}+y^{\prime }&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.290
12980	4224	\begin{align*} \cot \left (x \right ) y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.290
12981	8658	\begin{align*} y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\ \end{align*}	✓	✓	✓	✓	2.290
12982	21603	\begin{align*} y^{\prime }&=\frac {y+x^{2}+y^{2}}{x} \\ \end{align*}	✓	✓	✓	✓	2.290
12983	22802	\begin{align*} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	2.290
12984	23909	\begin{align*} y^{\prime }+x^{2} y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.290
12985	1704	\begin{align*} 3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.291
12986	4603	\begin{align*} y^{\prime \prime } x -2 y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	2.292
12987	8976	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.292
12988	12030	\begin{align*} y^{\prime }&=\frac {y \left (x +y\right )}{x \left (y^{3}+x \right )} \\ \end{align*}	✓	✓	✓	✗	2.292
12989	12896	\begin{align*} y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	2.292
12990	15537	\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}	✓	✓	✓	✓	2.292
12991	17523	\begin{align*} y^{\prime \prime }+y&=\tan \left (t \right )^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.292
12992	21404	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y&=x \,{\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✗	2.292
12993	12317	\begin{align*} y^{\prime \prime }+y^{\prime } x -n y&=0 \\ \end{align*}	✗	✓	✓	✗	2.293
12994	5462	\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✗	2.294
12995	8823	\begin{align*} 2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.294
12996	8878	\begin{align*} y^{\prime }+{\mathrm e}^{x} y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.294
12997	8677	\begin{align*} y^{\prime }&={\mathrm e}^{x -y} \\ \end{align*}	✓	✓	✓	✓	2.295
12998	20229	\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.295
12999	4996	\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \\ \end{align*}	✓	✓	✓	✓	2.296
13000	7363	\begin{align*} y^{\prime }&=3 x^{2} y \\ \end{align*}	✓	✓	✓	✓	2.296