2.3.154 Problems 15301 to 15400

Table 2.839: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15301	11567	\begin{align*} 2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.337
15302	17465	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=-{\mathrm e}^{3 t}-2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= {\frac {8}{9}} \\ \end{align*}	✓	✓	✓	✓	3.337
15303	19946	\begin{align*} y^{\prime }+\frac {4 x y}{x^{2}+1}&=\frac {1}{\left (x^{2}+1\right )^{3}} \\ \end{align*}	✓	✓	✓	✓	3.337
15304	686	\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=\left (1+y\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.338
15305	20308	\begin{align*} y \left (2 x^{2} y+{\mathrm e}^{x}\right )-\left ({\mathrm e}^{x}+y^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.338
15306	21565	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ \end{align*}	✓	✓	✓	✗	3.339
15307	24254	\begin{align*} 1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.339
15308	17169	\begin{align*} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y&=t \\ y \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	3.340
15309	6869	\begin{align*} y^{\prime } x -a y+y^{2}&=x^{-\frac {2 a}{3}} \\ \end{align*}	✓	✓	✓	✗	3.341
15310	2847	\begin{align*} \left (x +1\right ) y^{\prime }-1+y&=0 \\ \end{align*}	✓	✓	✓	✓	3.342
15311	5765	\begin{align*} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.342
15312	4334	\begin{align*} y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.343
15313	5611	\begin{align*} {y^{\prime }}^{3}&=\left (y-a \right )^{2} \left (y-b \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.343
15314	7264	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.344
15315	702	\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	3.345
15316	1696	\begin{align*} 4 x^{3} y^{2}-6 x^{2} y-2 x -3+\left (2 x^{4} y-2 x^{3}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}	✓	✓	✓	✗	3.345
15317	10399	\begin{align*} y^{\prime \prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	3.346
15318	1331	\begin{align*} 4 t^{2} y^{\prime \prime }-8 y^{\prime } t +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.347
15319	4618	\begin{align*} y^{\prime }&=a \,x^{n} y \\ \end{align*}	✓	✓	✓	✓	3.347
15320	12648	\begin{align*} y^{\prime \prime }&=-\frac {\left (a \,x^{2}+a -3\right ) y}{4 \left (x^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.347
15321	23031	\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}	✓	✓	✓	✓	3.347
15322	15781	\begin{align*} y^{\prime }&=2 t y^{2}+3 y^{2} \\ \end{align*}	✓	✓	✓	✓	3.348
15323	96	\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.349
15324	12269	\begin{align*} y^{\prime }&=-F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \\ \end{align*}	✓	✓	✓	✗	3.349
15325	13709	\begin{align*} y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{n +m}+b \,x^{2 m}+m \,x^{m -1}\right ) y&=0 \\ \end{align*}	✗	✗	✗	✗	3.349
15326	16245	\begin{align*} y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\ \end{align*}	✓	✓	✓	✗	3.349
15327	17460	\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-2 \\ y \left (0\right ) &= {\frac {2}{3}} \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}	✓	✓	✓	✓	3.349
15328	20298	\begin{align*} \left (x -y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}	✓	✓	✓	✓	3.349
15329	3558	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.352
15330	5787	\begin{align*} -4 y-3 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.352
15331	25528	\begin{align*} m y^{\prime \prime }+k y&=1 \\ \end{align*}	✓	✓	✓	✓	3.352
15332	1100	\begin{align*} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	3.355
15333	7525	\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\ \end{align*}	✓	✓	✓	✓	3.355
15334	23277	\begin{align*} y^{\prime \prime } x -3 y^{\prime }-5 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.355
15335	17183	\begin{align*} -\frac {y}{2}+y^{\prime }&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.357
15336	20776	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	3.357
15337	61	\begin{align*} 2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ y \left (5\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.358
15338	10327	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	3.358
15339	21790	\begin{align*} y^{\prime } x&=x +2 y \\ \end{align*}	✓	✓	✓	✓	3.358
15340	7354	\begin{align*} \sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2}&=r \cos \left (\theta \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.359
15341	19669	\begin{align*} x^{\prime }&=2 \sqrt {x} \\ x \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	3.359
15342	2565	\begin{align*} t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.360
15343	8246	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}	✓	✗	✗	✗	3.360
15344	14012	\begin{align*} \left (x +y\right ) y^{\prime }-1&=0 \\ \end{align*}	✓	✓	✓	✓	3.360
15345	15786	\begin{align*} y^{\prime }&=\frac {2 y+1}{t} \\ \end{align*}	✓	✓	✓	✓	3.361
15346	496	\begin{align*} x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	3.362
15347	4771	\begin{align*} y^{\prime } x +\left (-a \,x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.362
15348	24303	\begin{align*} x^{2}-2 y x -y^{2}-\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.362
15349	7735	\begin{align*} y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.364
15350	25099	\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.364
15351	5545	\begin{align*} y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✓	✗	3.365
15352	15830	\begin{align*} y^{\prime }&=t +t y \\ \end{align*}	✓	✓	✓	✓	3.365
15353	3592	\begin{align*} y^{\prime }&=2 y x \\ \end{align*}	✓	✓	✓	✓	3.367
15354	3630	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}&=9 x \\ \end{align*}	✓	✓	✓	✓	3.367
15355	7528	\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\ \end{align*}	✓	✓	✓	✓	3.367
15356	17860	\begin{align*} y^{\prime }&=x^{2}+2 x -y \\ \end{align*}	✓	✓	✓	✓	3.367
15357	3033	\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\ \end{align*}	✓	✗	✓	✗	3.368
15358	4880	\begin{align*} x^{2} y^{\prime }+2+a x \left (-y x +1\right )-y^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	3.368
15359	5782	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.368
15360	18586	\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.368
15361	20786	\begin{align*} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✗	✓	✓	✗	3.368
15362	23236	\begin{align*} y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{y} \\ \end{align*}	✓	✓	✓	✗	3.369
15363	6820	\begin{align*} y+x y^{2}-y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	3.370
15364	17227	\begin{align*} 1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\ y \left (2\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.370
15365	5346	\begin{align*} \left (a \cos \left (a y+b x \right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (a y+b x \right )-a \sin \left (a x +b y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	3.371
15366	21606	\begin{align*} y^{\prime }+x \left (-x +y\right )+x^{3} \left (-x +y\right )^{2}&=1 \\ \end{align*}	✓	✓	✓	✓	3.371
15367	14456	\begin{align*} y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.372
15368	4940	\begin{align*} x \left (x +1\right ) y^{\prime }&=\left (x +1\right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \\ \end{align*}	✓	✓	✓	✓	3.373
15369	15448	\begin{align*} y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.373
15370	16143	\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	3.373
15371	23008	\begin{align*} 35 y^{\prime \prime }-29 y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.373
15372	20282	\begin{align*} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \\ \end{align*}	✓	✓	✓	✗	3.374
15373	14127	\begin{align*} 4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.375
15374	23892	\begin{align*} x^{4}-3 y+3 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.375
15375	18517	\begin{align*} 4 t y+\left (t^{2}+1\right ) y^{\prime }&=\frac {1}{\left (t^{2}+1\right )^{2}} \\ \end{align*}	✓	✓	✓	✓	3.376
15376	774	\begin{align*} 2 x y^{3}+{\mathrm e}^{x}+\left (3 y^{2} x^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.377
15377	4584	\begin{align*} x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\ \end{align*}	✓	✓	✓	✓	3.378
15378	6311	\begin{align*} a \,{\mathrm e}^{y}+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.378
15379	14277	\begin{align*} x^{2}-t^{2} x^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.378
15380	23898	\begin{align*} 2 x y^{2}+2 x +\left (6 y^{3}+2 y+4 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	3.380
15381	11459	\begin{align*} \left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.381
15382	14193	\begin{align*} x^{\prime }&=-\frac {t}{x} \\ \end{align*}	✓	✓	✓	✓	3.382
15383	5830	\begin{align*} b y+a x y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✗	✓	✓	✗	3.383
15384	15541	\begin{align*} y^{\prime }&={| y|} \\ \end{align*}	✓	✓	✓	✓	3.383
15385	2560	\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	3.384
15386	5204	\begin{align*} 3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\ \end{align*}	✓	✓	✓	✓	3.384
15387	12351	\begin{align*} y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	3.384
15388	189	\begin{align*} x^{2} y^{\prime }&=y x +3 y^{2} \\ \end{align*}	✓	✓	✓	✓	3.385
15389	3315	\begin{align*} x&=y y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✗	3.385
15390	5727	\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \left (x^{2}-1\right ) \\ \end{align*}	✓	✓	✓	✓	3.385
15391	21602	\begin{align*} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u&=0 \\ u \left (1\right ) &= -1 \\ u^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	3.386
15392	19388	\begin{align*} y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\ \end{align*}	✓	✓	✓	✓	3.387
15393	4972	\begin{align*} x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\ \end{align*}	✓	✓	✓	✓	3.388
15394	5231	\begin{align*} \left (x -y\right )^{2} y^{\prime }&=\left (-x -y+1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	3.388
15395	7583	\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}	✓	✓	✓	✓	3.388
15396	25087	\begin{align*} y^{\prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \\ \end{align*}	✓	✓	✓	✓	3.388
15397	5286	\begin{align*} x \left (-y x +1\right )^{2} y^{\prime }+\left (1+y^{2} x^{2}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	3.389
15398	19921	\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	3.390
15399	22332	\begin{align*} y^{\prime }&=y^{3} \\ \end{align*}	✓	✓	✓	✓	3.390
15400	12057	\begin{align*} y^{\prime }&=\frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \\ \end{align*}	✓	✓	✓	✗	3.391