Differential Equation in circuit question

[scarlets99]

Homework Statement

In a circuit with capacitance C, inductance L and resistance R the current I(t)
satisfies the differential equation

L d2I(t)/dt2 + R dI(t)/dt + I(t)/C = V(t)

where V (t)
is the voltage supplied.
a) Find the general solution to this differential equation
for the case that the resistance can be neglected, R = 0,
and the voltage is constant, V (t) = V0.
b) Determine the solution of part a) that satisfies the initial conditions I(0) = 0 and dI/dt(0) = 0

Homework Equations

The Attempt at a Solution

As this is a linear second order ODE, with constant coefficients, I have tried calculating the homogeneous equation (place V(t)=0) but cannot seem to get an answer, and I am not sure what ansatz to use.

please help

 

[vela]

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