second order ode const coeﬀ

2.5.9 second order ode const coeﬀ

Table 2.1153: second order ode const coeﬀ [56]


#	ODE	CAS classiﬁcation	Solved	Maple	Mma	Sympy	time(sec)

260	\begin{align} y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.204

261	\begin{align} y^{\prime \prime }+2 y&=6 x +4 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.132

311	\begin{align} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.060

322	\begin{align} y^{\prime \prime }+16 y&={\mathrm e}^{3 x} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.120

323	\begin{align} y^{\prime \prime }-y^{\prime }+2 y&=3 x +4 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.136

324	\begin{align} y^{\prime \prime }-y^{\prime }-6 y&=2 \sin \left (3 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.147

325	\begin{align} 4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.127

326	\begin{align} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right )^{2} \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.178

327	\begin{align} 2 y^{\prime \prime }+4 y^{\prime }+7 y&=x^{2} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.139

328	\begin{align} y^{\prime \prime }-4 y&=\sinh \left (x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.200

329	\begin{align} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.233

330	\begin{align} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.146

331	\begin{align} 2 y^{\prime \prime }+9 y&=2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.168

353	\begin{align} y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.226

355	\begin{align} y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.209

358	\begin{align} y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (3 x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.248

365	\begin{align} y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.316

366	\begin{align} 2 y+3 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.125

367	\begin{align} y^{\prime \prime }-2 y^{\prime }-8 y&=3 \,{\mathrm e}^{-2 x} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.132

368	\begin{align} y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{2 x} \\ \end{align}	[[_2nd_order, _with_linear_symmetries]]	✓	✓	✓	✓	0.124

369	\begin{align} y^{\prime \prime }-4 y&=\sinh \left (2 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.220

370	\begin{align} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.136

371	\begin{align} y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.141

375	\begin{align} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.127

382	\begin{align} y^{\prime \prime }+y&=2 \sin \left (x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.125

384	\begin{align} x^{\prime \prime }+4 x&=5 \sin \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.229

385	\begin{align} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\ x \left (0\right ) &= 375 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.263

387	\begin{align} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.347

388	\begin{align} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.142

389	\begin{align} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.169

390	\begin{align} 2 x^{\prime \prime }+2 x^{\prime }+x&=3 \sin \left (10 t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.171

391	\begin{align} x^{\prime \prime }+3 x^{\prime }+3 x&=8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.192

392	\begin{align} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.255

393	\begin{align} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.280

394	\begin{align} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.294

395	\begin{align} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \\ x \left (0\right ) &= -30 \\ x^{\prime }\left (0\right ) &= -10 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.254

396	\begin{align} x^{\prime \prime }+2 x^{\prime }+2 x&=2 \cos \left (\omega t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.142

397	\begin{align} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (\omega t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.147

398	\begin{align} x^{\prime \prime }+6 x^{\prime }+45 x&=50 \cos \left (\omega t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.150

399	\begin{align} x^{\prime \prime }+10 x^{\prime }+650 x&=100 \cos \left (\omega t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.152

859	\begin{align} y^{\prime \prime }&=\left (-2+2 i \sqrt {3}\right ) y \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.065

12287	\begin{align} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}&=0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.206

12288	\begin{align} y^{\prime \prime }+a^{2} y-\cot \left (a x \right )&=0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.817

12311	\begin{align} y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right )&=0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.348

12339	\begin{align} y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y&=0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	1.573

14639	\begin{align} 4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.793

17470	\begin{align} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	6.633

17471	\begin{align} y^{\prime \prime }+9 \pi ^{2} y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	28.513

17814	\begin{align} x^{\prime \prime }+x&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	4.176

17815	\begin{align} x^{\prime \prime }+4 x^{\prime }+13 x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	18.386

22690	\begin{align} 4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.681

22717	\begin{align} 4 y+y^{\prime \prime }&=x^{2}+3 x \cos \left (2 x \right ) \\ \end{align}	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓	✓	✓	0.524

23019	\begin{align} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right ) &= 4 \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.277

23022	\begin{align} y^{\prime \prime }+3 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y \left (\frac {\pi \sqrt {3}}{3}\right ) &= 5 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{2}} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.313

23023	\begin{align} x^{\prime \prime }+2 x^{\prime }+4 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi \sqrt {3}}{6}\right ) &= 2 \,{\mathrm e}^{-\frac {\pi \sqrt {3}}{6}} \\ \end{align}	[[_2nd_order, _missing_x]]	✓	✓	✓	✓	0.310

23762	\begin{align} y^{\prime \prime }&=0 \\ y \left (0\right ) &= \operatorname {c1} \\ y \left (L \right ) &= \operatorname {c2} \\ \end{align}	[[_2nd_order, _quadrature]]	✓	✓	✓	✓	0.199

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