2.3.142 Problems 14101 to 14200

Table 2.833: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
14101	5753	\begin{align*} y^{\prime \prime }&=2 \csc \left (x \right )^{2} y \\ \end{align*}	✓	✓	✓	✗	1.522
14102	9180	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.522
14103	17079	\begin{align*} y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	1.522
14104	18096	\begin{align*} y^{\prime \prime } x&=y^{\prime }+x^{2} \\ \end{align*}	✓	✓	✓	✓	1.522
14105	206	\begin{align*} y^{\prime } x +y&=2 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	1.523
14106	7207	\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.523
14107	9871	\begin{align*} 2 y^{\prime \prime } x +\left (2 x +1\right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.523
14108	5887	\begin{align*} \left (a +x \right ) y+y^{\prime \prime } x&=0 \\ \end{align*}	✗	✓	✓	✗	1.524
14109	14388	\begin{align*} x^{\prime }&=2 x+3 y \\ y^{\prime }&=-x-14 \\ \end{align*}	✓	✓	✓	✓	1.524
14110	4739	\begin{align*} y^{\prime }&=a f \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.525
14111	8132	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.525
14112	11378	\begin{align*} y^{\prime }-\cos \left (a y+b x \right )&=0 \\ \end{align*}	✓	✓	✓	✓	1.525
14113	6060	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.526
14114	7799	\begin{align*} y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.526
14115	5626	\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\ \end{align*}	✓	✓	✓	✗	1.527
14116	5698	\begin{align*} \left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.527
14117	4486	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.528
14118	8148	\begin{align*} x^{2} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.528
14119	19440	\begin{align*} y^{\prime \prime }+y^{\prime }&=0 \\ y \left (2\right ) &= 0 \\ y^{\prime }\left (2\right ) &= {\mathrm e}^{-2} \\ \end{align*}	✓	✓	✓	✓	1.528
14120	8652	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.529
14121	9557	\begin{align*} y^{\prime \prime } x +\left (x -6\right ) y^{\prime }-3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.529
14122	11355	\begin{align*} y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.529
14123	15660	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.529
14124	18192	\begin{align*} y^{\prime \prime }+8 y^{\prime }&=8 x \\ \end{align*}	✓	✓	✓	✓	1.529
14125	20507	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.529
14126	4088	\begin{align*} -x +y&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \\ \end{align*}	✓	✓	✓	✗	1.530
14127	8095	\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.530
14128	16698	\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✗	1.530
14129	22768	\begin{align*} \left (3+2 x \right )^{2} y^{\prime \prime }+\left (3+2 x \right ) y^{\prime }-2 y&=24 x^{2} \\ \end{align*}	✓	✓	✓	✗	1.530
14130	4138	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.531
14131	8022	\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{2}} \\ \end{align*}	✓	✓	✓	✓	1.531
14132	11760	\begin{align*} \left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2&=0 \\ \end{align*}	✓	✓	✓	✗	1.532
14133	15549	\begin{align*} y^{\prime }&=\ln \left (-1+y\right ) \\ \end{align*}	✓	✓	✓	✓	1.532
14134	14659	\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	1.533
14135	23402	\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x -1}+\frac {4 y}{\left (x -1\right )^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.533
14136	25232	\begin{align*} t^{2} y^{\prime \prime }-3 y^{\prime } t +13 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.533
14137	2074	\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.534
14138	2707	\begin{align*} x^{\prime }&=2 x-5 y+\sin \left (t \right ) \\ y^{\prime }&=x-2 y+\tan \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.534
14139	9922	\begin{align*} x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (5 x +1\right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.534
14140	13791	\begin{align*} x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (1+a \right )\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.534
14141	20134	\begin{align*} y^{\prime \prime }-a {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.534
14142	4483	\begin{align*} y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \\ \end{align*}	✓	✓	✓	✓	1.535
14143	5711	\begin{align*} y^{\prime \prime }&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.535
14144	7655	\begin{align*} y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+\cos \left (x \right ) y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.535
14145	19367	\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✗	✗	1.535
14146	9758	\begin{align*} 5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.536
14147	12328	\begin{align*} y^{\prime \prime }+2 a x y^{\prime }+y a^{2} x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.536
14148	12861	\begin{align*} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right )&=0 \\ \end{align*}	✗	✗	✗	✗	1.536
14149	14840	\begin{align*} t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	1.536
14150	20034	\begin{align*} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}-b^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.536
14151	25807	\begin{align*} y^{\prime }&=10+3 y-y^{2} \\ \end{align*}	✓	✓	✓	✓	1.536
14152	8405	\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.537
14153	9276	\begin{align*} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=x \left (x +1\right )^{2} \\ \end{align*}	✓	✓	✓	✗	1.537
14154	13294	\begin{align*} y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\ \end{align*}	✓	✓	✓	✗	1.537
14155	16106	\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 t +{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.537
14156	20471	\begin{align*} {y^{\prime }}^{3}&=y^{4} \left (y^{\prime } x +y\right ) \\ \end{align*}	✓	✓	✓	✗	1.537
14157	4461	\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&={\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \\ \end{align*}	✓	✓	✓	✓	1.538
14158	7193	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.539
14159	7196	\begin{align*} \left (1-x \right ) x y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.539
14160	9256	\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}	✓	✓	✓	✓	1.540
14161	20501	\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x&=\ln \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.540
14162	6958	\begin{align*} y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.541
14163	10113	\begin{align*} y^{\prime \prime }-x^{2} y-x^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.541
14164	13929	\begin{align*} y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.541
14165	7210	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.542
14166	17488	\begin{align*} y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.542
14167	17533	\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=t^{3}+2 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✗	✗	1.542
14168	24823	\begin{align*} {y^{\prime }}^{3}-y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.542
14169	2542	\begin{align*} 2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.543
14170	10115	\begin{align*} y^{\prime \prime }-x^{2} y-x^{4}&=0 \\ \end{align*}	✓	✓	✓	✗	1.543
14171	15485	\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✓	1.543
14172	16178	\begin{align*} \cos \left (x \right ) y^{\prime }-\sin \left (x \right )&=0 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	1.543
14173	9220	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.544
14174	10116	\begin{align*} y^{\prime \prime }-x^{2} y-x^{4}+2&=0 \\ \end{align*}	✓	✓	✓	✗	1.544
14175	18154	\begin{align*} y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\ \end{align*}	✓	✓	✓	✓	1.544
14176	18393	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +4 \left (x^{4}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	1.544
14177	3399	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y&=x^{2} \left (2+x \right )^{2} \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.545
14178	14025	\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.545
14179	20729	\begin{align*} x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\ \end{align*}	✓	✓	✓	✓	1.545
14180	5572	\begin{align*} y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\ \end{align*}	✓	✓	✓	✗	1.546
14181	9944	\begin{align*} 2 y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.546
14182	23926	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=2 x \\ \end{align*}	✓	✓	✓	✓	1.546
14183	9416	\begin{align*} \left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=3\).	✓	✓	✓	✓	1.548
14184	17453	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\ \end{align*}	✓	✓	✓	✓	1.548
14185	6	\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.549
14186	19685	\begin{align*} x^{\prime }&=-\lambda x \\ \end{align*}	✓	✓	✓	✓	1.549
14187	10308	\begin{align*} {y^{\prime }}^{2}&=x +y \\ \end{align*}	✓	✓	✓	✓	1.550
14188	684	\begin{align*} y^{\prime }&=2 x \sec \left (y\right ) \\ \end{align*}	✓	✓	✓	✓	1.551
14189	5823	\begin{align*} -8 y+2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.551
14190	7455	\begin{align*} \left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.551
14191	8137	\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.553
14192	19148	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\ \end{align*}	✓	✓	✓	✗	1.553
14193	22660	\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.553
14194	2374	\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t -2 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.554
14195	5990	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.554
14196	7375	\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.554
14197	12366	\begin{align*} y^{\prime \prime } x +2 y^{\prime }-y x -{\mathrm e}^{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.554
14198	819	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.555
14199	5535	\begin{align*} x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\ \end{align*}	✓	✓	✓	✓	1.555
14200	6054	\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.555