2.3.152 Problems 15101 to 15200

Table 2.877: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15101	25427	\begin{align*} -2 y+y^{\prime }&={\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.417
15102	1916	\begin{align*} \left (\beta \,x^{2}+x \alpha +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.418
15103	4227	\begin{align*} y^{\prime } x&=y x +y \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.418
15104	4296	\begin{align*} \ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\ \end{align*}	✓	✓	✓	✓	1.418
15105	12285	\begin{align*} y^{\prime \prime }+y-\sin \left (a x \right ) \sin \left (b x \right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.418
15106	510	\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.419
15107	24459	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.419
15108	1330	\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}	✓	✓	✓	✓	1.420
15109	1549	\begin{align*} y^{\prime }+\left (\frac {1}{x}-1\right ) y&=-\frac {2}{x} \\ \end{align*}	✓	✓	✓	✓	1.421
15110	6129	\begin{align*} 2 y-\left (2+x \right ) y^{\prime }+\left (2+x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.421
15111	6132	\begin{align*} 6 y-4 \left (a +x \right ) y^{\prime }+\left (a +x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.421
15112	8462	\begin{align*} y^{\prime }-2 y x&=1 \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.421
15113	16925	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y&=0 \\ \end{align*} Series expansion around \(x=1\).	✓	✓	✓	✗	1.421
15114	3565	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.422
15115	5963	\begin{align*} -\left (n \left (n +1\right )+a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.422
15116	15808	\begin{align*} y^{\prime }&=\frac {y^{2}+5}{y} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.422
15117	18950	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.422
15118	17352	\begin{align*} 2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.423
15119	22519	\begin{align*} y^{\prime }&=x +y \\ \end{align*}	✓	✓	✓	✓	1.423
15120	8448	\begin{align*} L i^{\prime }+R i&=E \\ i \left (0\right ) &= i_{0} \\ \end{align*}	✓	✓	✓	✓	1.424
15121	15404	\begin{align*} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✗	1.424
15122	18894	\begin{align*} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 9 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.424
15123	21045	\begin{align*} x^{\prime }&={\mathrm e}^{x}-t \\ \end{align*}	✓	✓	✓	✓	1.424
15124	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*}	✓	✓	✓	✓	1.424
15125	3982	\begin{align*} y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.425
15126	18740	\begin{align*} y^{\prime \prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.425
15127	18952	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.425
15128	27171	\begin{align*} x_{1}^{\prime }&=2 x_{1}-3 x_{2}+x_{3}+10 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{2}+4 x_{3}+6 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }&=x_{3}-{\mathrm e}^{2 t} \\ \end{align*} With initial conditions \begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 11 \\ x_{3} \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.425
15129	11321	\begin{align*} y^{\prime }-\left (x +y\right )^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.428
15130	14133	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\ \end{align*}	✓	✓	✓	✗	1.428
15131	20714	\begin{align*} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\ \end{align*}	✓	✓	✓	✓	1.428
15132	27353	\begin{align*} y^{2} \left (1+{y^{\prime }}^{2}\right )&=1 \\ \end{align*}	✓	✓	✓	✓	1.428
15133	8247	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.429
15134	667	\begin{align*} y^{\prime }&=x^{2}-y \\ \end{align*}	✓	✓	✓	✓	1.430
15135	11775	\begin{align*} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.430
15136	18949	\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.430
15137	20897	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+\frac {3 y^{\prime }}{2+x}+\frac {\left (1-x \right )^{2} y}{x +3}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.430
15138	6202	\begin{align*} y a \,x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.431
15139	16705	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.431
15140	21093	\begin{align*} x^{\prime }-t x&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.431
15141	24268	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	1.431
15142	9887	\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.432
15143	16416	\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.433
15144	1741	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ y \left (0\right ) &= -5 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.434
15145	7902	\begin{align*} y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.434
15146	14168	\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \\ \end{align*}	✓	✓	✓	✓	1.434
15147	16612	\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\ \end{align*}	✓	✓	✓	✓	1.434
15148	24570	\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }-3 y&=-9 x^{2}-1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.434
15149	9244	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.435
15150	12346	\begin{align*} \left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.435
15151	17482	\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \\ \end{align*}	✓	✓	✓	✓	1.435
15152	18956	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.435
15153	25725	\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.435
15154	199	\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y&=1 \\ \end{align*}	✓	✓	✓	✓	1.436
15155	2320	\begin{align*} y^{\prime }&={\mathrm e}^{3+t +y} \\ \end{align*}	✓	✓	✓	✓	1.436
15156	20385	\begin{align*} {y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1&=0 \\ \end{align*}	✓	✓	✓	✓	1.436
15157	3575	\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.437
15158	5535	\begin{align*} x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\ \end{align*}	✓	✓	✓	✓	1.437
15159	8334	\begin{align*} y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\ \end{align*}	✓	✓	✓	✓	1.437
15160	14413	\begin{align*} y^{\prime }+y&=x +1 \\ \end{align*}	✓	✓	✓	✓	1.437
15161	17716	\begin{align*} y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.437
15162	9886	\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.438
15163	24472	\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.438
15164	8040	\begin{align*} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \\ \end{align*}	✓	✓	✓	✗	1.439
15165	21670	\begin{align*} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✗	1.439
15166	23063	\begin{align*} r^{\prime }&=c \\ r \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.439
15167	10284	\begin{align*} y^{\prime }&=y+\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.440
15168	16409	\begin{align*} y^{\prime \prime } x&=-y^{\prime }+{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	1.440
15169	24578	\begin{align*} a^{2} y+y^{\prime \prime }&=\sin \left (a x \right ) \\ \end{align*}	✓	✓	✓	✓	1.440
15170	28	\begin{align*} y^{\prime }&=\ln \left (y\right ) x \\ y \left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.441
15171	1513	\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.441
15172	3698	\begin{align*} y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.441
15173	5711	\begin{align*} y^{\prime \prime }&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.441
15174	8216	\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.441
15175	9754	\begin{align*} 2 {y^{\prime }}^{2}+y^{\prime } x -2 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.441
15176	10324	\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}	✓	✓	✓	✓	1.441
15177	14053	\begin{align*} y^{\prime }+2 y x&=x^{2}+y^{2} \\ \end{align*}	✓	✓	✓	✓	1.441
15178	15590	\begin{align*} 2 y y^{\prime }&=1 \\ \end{align*}	✓	✓	✓	✓	1.441
15179	16922	\begin{align*} y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.441
15180	2839	\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.442
15181	12973	\begin{align*} a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}}&=0 \\ \end{align*}	✓	✓	✓	✗	1.442
15182	15515	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.442
15183	19889	\begin{align*} z^{\prime }+5 y-2 z&=x \\ y^{\prime }+4 y+z&=x \\ \end{align*}	✓	✓	✓	✓	1.442
15184	25481	\begin{align*} y^{\prime }&=2 \left (1-y\right ) \left (1-{\mathrm e}^{y}\right ) \\ \end{align*}	✓	✓	✓	✓	1.442
15185	27607	\begin{align*} 2 y^{\prime \prime \prime }-3 {y^{\prime }}^{2}&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ \end{align*}	✗	✓	✗	✗	1.442
15186	1119	\begin{align*} -y+2 y^{\prime }&={\mathrm e}^{\frac {t}{3}} \\ y \left (0\right ) &= a \\ \end{align*}	✓	✓	✓	✓	1.443
15187	8175	\begin{align*} y^{\prime } x -3 y x&=1 \\ \end{align*}	✓	✓	✓	✓	1.443
15188	27380	\begin{align*} y&={y^{\prime }}^{2}+2 {y^{\prime }}^{3} \\ \end{align*}	✓	✓	✗	✓	1.443
15189	9626	\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	1.444
15190	16048	\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=-2 y+3 z \\ z^{\prime }&=-x+3 y-z \\ \end{align*}	✓	✓	✓	✓	1.444
15191	16961	\begin{align*} 2 x -1-y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.444
15192	24830	\begin{align*} x {y^{\prime }}^{2}+y y^{\prime }&=3 y^{4} \\ \end{align*}	✓	✓	✓	✓	1.444
15193	4035	\begin{align*} x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 \,{\mathrm e}^{x} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.445
15194	19703	\begin{align*} y^{\prime }+c y&=a \\ \end{align*}	✓	✓	✓	✓	1.445
15195	7355	\begin{align*} x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )&=y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.447
15196	10415	\begin{align*} y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \\ \end{align*}	✗	✓	✓	✗	1.447
15197	15083	\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✗	1.447
15198	17378	\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=0 \\ y \left (\pi \right ) &= 0 \\ y \left (2 \pi \right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.447
15199	18784	\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.447
15200	23099	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.447