2.4.1 second order ode quadrature

Table 2.375: second order ode quadrature

#

ODE

CAS classification

Solved?

11

\[ {}x^{\prime \prime } = 50 \]
i.c.

[[_2nd_order, _quadrature]]

12

\[ {}x^{\prime \prime } = -20 \]
i.c.

[[_2nd_order, _quadrature]]

13

\[ {}x^{\prime \prime } = 3 t \]
i.c.

[[_2nd_order, _quadrature]]

14

\[ {}x^{\prime \prime } = 2 t +1 \]
i.c.

[[_2nd_order, _quadrature]]

15

\[ {}x^{\prime \prime } = 4 \left (t +3\right )^{2} \]
i.c.

[[_2nd_order, _quadrature]]

16

\[ {}x^{\prime \prime } = \frac {1}{\sqrt {t +4}} \]
i.c.

[[_2nd_order, _quadrature]]

17

\[ {}x^{\prime \prime } = \frac {1}{\left (1+t \right )^{3}} \]
i.c.

[[_2nd_order, _quadrature]]

18

\[ {}x^{\prime \prime } = 50 \sin \left (5 t \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3022

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

3177

\[ {}y^{\prime \prime } = \cos \left (t \right ) \]

[[_2nd_order, _quadrature]]

3182

\[ {}x y^{\prime \prime } = x^{2}+1 \]

[[_2nd_order, _quadrature]]

3205

\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3517

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

3518

\[ {}y^{\prime \prime } = x^{n} \]

[[_2nd_order, _quadrature]]

3520

\[ {}y^{\prime \prime } = \cos \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

3522

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _quadrature]]

5505

\[ {}y^{\prime \prime } = 0 \]
i.c.

[[_2nd_order, _quadrature]]

6074

\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \]

[[_2nd_order, _quadrature]]

6817

\[ {}y^{\prime \prime } = x +2 \]

[[_2nd_order, _quadrature]]

6825

\[ {}y^{\prime \prime } = 3 x +1 \]

[[_2nd_order, _quadrature]]

6851

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

7289

\[ {}y^{\prime \prime } = \tan \left (x \right ) \]
i.c.

[[_2nd_order, _quadrature]]

8002

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

8003

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

8004

\[ {}y^{\prime \prime } = f \left (t \right ) \]

[[_2nd_order, _quadrature]]

8005

\[ {}y^{\prime \prime } = k \]

[[_2nd_order, _quadrature]]

8008

\[ {}y^{\prime \prime } = 4 \sin \left (x \right )-4 \]

[[_2nd_order, _quadrature]]

8294

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

8297

\[ {}a y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

8300

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

8302

\[ {}y^{\prime \prime } = x \]

[[_2nd_order, _quadrature]]

10233

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

12213

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]

[[_2nd_order, _quadrature]]

12260

\[ {}x^{\prime \prime } = -3 \sqrt {t} \]
i.c.

[[_2nd_order, _quadrature]]

14146

\[ {}y^{\prime \prime } = \frac {x +1}{x -1} \]

[[_2nd_order, _quadrature]]

14147

\[ {}x^{2} y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

14160

\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \]

[[_2nd_order, _quadrature]]

14161

\[ {}y^{\prime \prime }-3 = x \]

[[_2nd_order, _quadrature]]

14169

\[ {}x y^{\prime \prime }+2 = \sqrt {x} \]
i.c.

[[_2nd_order, _quadrature]]

14612

\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \]

[[_2nd_order, _quadrature]]

15368

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

15423

\[ {}y^{\prime \prime } = 3 t^{4}-2 t \]

[[_2nd_order, _quadrature]]

15445

\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \]

[[_2nd_order, _quadrature]]

16071

\[ {}\left (x -1\right ) y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

16079

\[ {}y^{\prime \prime } \left (x +2\right )^{5} = 1 \]
i.c.

[[_2nd_order, _quadrature]]

16080

\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \]
i.c.

[[_2nd_order, _quadrature]]

16081

\[ {}y^{\prime \prime } = 2 x \ln \left (x \right ) \]

[[_2nd_order, _quadrature]]