2.3.164 Problems 16301 to 16400

Table 2.901: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
16301	7432	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+y x -x&=0 \\ \end{align*}	✓	✓	✓	✓	2.275
16302	13691	\begin{align*} y^{\prime \prime }+2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	2.275
16303	15893	\begin{align*} y^{\prime }&=y \sin \left (\frac {\pi y}{2}\right ) \\ \end{align*}	✓	✓	✓	✓	2.275
16304	25532	\begin{align*} y^{\prime }&=a y \\ \end{align*}	✓	✓	✓	✓	2.276
16305	18013	\begin{align*} y&=2 x y^{\prime }+\sin \left (y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✗	2.279
16306	26463	\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.279
16307	10428	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-c^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.282
16308	15935	\begin{align*} v^{\prime }+\frac {2 v}{5}&=3 \cos \left (2 t \right ) \\ \end{align*}	✓	✓	✓	✓	2.282
16309	19947	\begin{align*} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.282
16310	25420	\begin{align*} -y+y^{\prime }&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.282
16311	177	\begin{align*} x^{\prime }&=4 x \left (7-x\right ) \\ x \left (0\right ) &= 11 \\ \end{align*}	✓	✓	✓	✓	2.283
16312	11684	\begin{align*} {y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.283
16313	26204	\begin{align*} y^{\prime }&=\frac {y}{x} \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.283
16314	14717	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.284
16315	3560	\begin{align*} y^{\prime }&=-y^{2} \\ \end{align*}	✓	✓	✓	✓	2.285
16316	5773	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x}+x^{2}-\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.285
16317	15168	\begin{align*} x y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	2.285
16318	8276	\begin{align*} y^{\prime }-2 y x&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	2.286
16319	15907	\begin{align*} y+y^{\prime }&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.286
16320	21437	\begin{align*} y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	2.286
16321	21488	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.286
16322	27270	\begin{align*} \left (x +y^{2}\right ) y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	2.286
16323	89	\begin{align*} \left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.287
16324	2634	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.287
16325	8449	\begin{align*} T^{\prime }&=k \left (T-T_{m} \right ) \\ T \left (0\right ) &= T_{0} \\ \end{align*}	✓	✓	✓	✓	2.287
16326	21022	\begin{align*} x^{\prime }-2 x&=2 t \\ x \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.287
16327	27488	\begin{align*} y^{\prime }&=-\tan \left (2 x -y\right ) \\ \end{align*}	✓	✓	✓	✓	2.287
16328	20666	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y&=0 \\ \end{align*}	✓	✓	✓	✗	2.288
16329	27531	\begin{align*} y y^{\prime \prime }+1&={y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	2.288
16330	16214	\begin{align*} y^{\prime }+4 y&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.289
16331	16564	\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	2.289
16332	17360	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.289
16333	20198	\begin{align*} -y+x y^{\prime }+y^{\prime \prime }&=f \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	2.289
16334	22946	\begin{align*} x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t} \\ y^{\prime }-2 x-5 y+3 z&=0 \\ z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	2.289
16335	7953	\begin{align*} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.290
16336	6686	\begin{align*} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}	✗	✓	✗	✗	2.292
16337	14081	\begin{align*} {y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\ \end{align*}	✓	✓	✓	✓	2.292
16338	24253	\begin{align*} 2 y&=\left (x^{2}-1\right ) \left (1-y^{\prime }\right ) \\ \end{align*}	✓	✓	✓	✓	2.292
16339	5983	\begin{align*} -\left (i x^{2}+p^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.294
16340	7703	\begin{align*} y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	2.294
16341	17141	\begin{align*} -y+y^{\prime }&=t^{2}-2 t \\ \end{align*}	✓	✓	✓	✓	2.294
16342	7878	\begin{align*} y^{2}+y x -x y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.295
16343	16379	\begin{align*} y^{\prime }&=x \left (6 y+{\mathrm e}^{x^{2}}\right ) \\ \end{align*}	✓	✓	✓	✓	2.295
16344	763	\begin{align*} x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.296
16345	24841	\begin{align*} y^{2} {y^{\prime }}^{3}-x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✗	✗	2.296
16346	4124	\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.297
16347	11759	\begin{align*} \left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	2.297
16348	19253	\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \\ \end{align*}	✓	✓	✓	✓	2.297
16349	21318	\begin{align*} x^{\prime \prime }-x^{3}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}	✓	✓	✓	✗	2.297
16350	12426	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+a y&=0 \\ \end{align*}	✓	✓	✓	✓	2.298
16351	15123	\begin{align*} y^{\prime }&=\ln \left (y x \right ) \\ \end{align*}	✗	✗	✗	✗	2.298
16352	671	\begin{align*} y^{\prime }&=y^{{1}/{3}} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	2.299
16353	7217	\begin{align*} x y^{\prime }&=y \\ y \left (2\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.299
16354	11948	\begin{align*} y^{\prime }&=-\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\ \end{align*}	✗	✓	✓	✓	2.299
16355	11462	\begin{align*} 2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x&=0 \\ \end{align*}	✓	✓	✓	✗	2.300
16356	23166	\begin{align*} y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\ \end{align*}	✓	✓	✓	✓	2.301
16357	25460	\begin{align*} y^{\prime }&=y+2 t \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.301
16358	1202	\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.302
16359	2372	\begin{align*} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y&=0 \\ \end{align*}	✓	✓	✓	✓	2.302
16360	14205	\begin{align*} x^{\prime \prime }&=-3 \sqrt {t} \\ x \left (1\right ) &= 4 \\ x^{\prime }\left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	2.302
16361	27528	\begin{align*} y^{3} y^{\prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	2.302
16362	8203	\begin{align*} {y^{\prime }}^{2} x -4 y^{\prime }-12 x^{3}&=0 \\ \end{align*}	✓	✓	✓	✓	2.303
16363	11460	\begin{align*} \left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	2.303
16364	709	\begin{align*} 2 x y^{\prime }+y&=10 \sqrt {x} \\ y \left (2\right ) &= 5 \\ \end{align*}	✓	✓	✓	✓	2.304
16365	12448	\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x&=0 \\ \end{align*}	✓	✓	✓	✓	2.304
16366	21950	\begin{align*} t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t}&=t^{2}-t +1 \\ \end{align*}	✓	✓	✓	✗	2.304
16367	13009	\begin{align*} \left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✗	✓	✓	✗	2.305
16368	2565	\begin{align*} t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.306
16369	1103	\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	2.307
16370	7039	\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✓	2.307
16371	8445	\begin{align*} y^{\prime }&=2 x -3 y \\ y \left (0\right ) &= {\frac {1}{3}} \\ \end{align*}	✓	✓	✓	✓	2.308
16372	23201	\begin{align*} 2 x^{2}+2 y^{2}+x +\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.308
16373	19406	\begin{align*} x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\ \end{align*}	✓	✓	✓	✓	2.309
16374	21687	\begin{align*} 2 \left (1-x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x -3-\left (x -1\right )^{2} {\mathrm e}^{x}\right ) y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✓	2.309
16375	23955	\begin{align*} y^{\prime }&=\frac {y}{y-y^{3}+2 x} \\ \end{align*}	✓	✓	✓	✗	2.309
16376	25406	\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	2.309
16377	8195	\begin{align*} y y^{\prime }+\sqrt {16-y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	2.310
16378	26281	\begin{align*} \left (a^{2}-x^{2}\right ) y^{\prime }+y x&=a^{2} \\ \end{align*}	✓	✓	✓	✓	2.310
16379	13288	\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2} \\ \end{align*}	✓	✓	✓	✗	2.311
16380	1180	\begin{align*} y^{\prime }&=-y \left (3-y t \right ) \\ \end{align*}	✓	✓	✓	✓	2.312
16381	6407	\begin{align*} x^{4} y^{\prime \prime }&=-4 y^{2}+x \left (x^{2}+2 y\right ) y^{\prime } \\ \end{align*}	✗	✓	✓	✗	2.312
16382	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*}	✓	✓	✓	✓	2.312
16383	20691	\begin{align*} a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	2.312
16384	22061	\begin{align*} y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	2.313
16385	22481	\begin{align*} i^{\prime \prime }&=t^{2}+1 \\ i \left (0\right ) &= 2 \\ i^{\prime }\left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	2.313
16386	5556	\begin{align*} \left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.314
16387	102	\begin{align*} 2 x y^{\prime }&=y+2 x \cos \left (x \right ) \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	2.316
16388	168	\begin{align*} y^{\prime }+2 y x&=1+x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	2.316
16389	6952	\begin{align*} \arctan \left (y x \right )+\frac {y x -2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	2.316
16390	15087	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=\frac {y y^{\prime }}{\sqrt {x^{2}+1}} \\ \end{align*}	✓	✓	✓	✗	2.318
16391	14153	\begin{align*} 2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\ \end{align*}	✓	✓	✓	✗	2.319
16392	25297	\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	2.319
16393	26230	\begin{align*} x^{2} y^{3}+y+x -2+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.320
16394	1139	\begin{align*} x +y y^{\prime } {\mathrm e}^{-x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.321
16395	25292	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✗	✓	✗	2.322
16396	6039	\begin{align*} -2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	2.323
16397	8462	\begin{align*} y^{\prime }-2 y x&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	2.323
16398	19730	\begin{align*} {y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✗	2.323
16399	24981	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	2.323
16400	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*}	✓	✓	✓	✓	2.325