2.4.24 second order ode time varying using laplace

Table 2.473: second order ode time varying using laplace

#

ODE

CAS classification

Solved?

555

\[ {}t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

556

\[ {}t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x = 0 \]
i.c.

[[_2nd_order, _exact, _linear, _homogeneous]]

557

\[ {}t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

558

\[ {}t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

559

\[ {}t x^{\prime \prime }-2 x^{\prime }+x t = 0 \]
i.c.

[_Lienard]

560

\[ {}t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

15274

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

[_Lienard]

18134

\[ {}x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

18135

\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x} \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

18136

\[ {}y^{\prime \prime }+x^{2} y = 0 \]
i.c.

[[_Emden, _Fowler]]