# Math Help - [SOLVED] Second order differential equations

1. ## [SOLVED] Second order differential equations

a)
Find the general solution of the second order differential equation
4
y′′ + 8y+ 3y = 0 .

Find the particular solution that satisfies the initial conditions y(0) = 2 and y(0) = 1/2.

I got the general solution to be:

y(x) = (c^(A))e^((-3/2)x)+(c^(B))e^((-1/2)x)

and by intitial condiotion I got the particular solution to be:

y(x) = (-3/2)e^((-3/2)x)+(7/2)e^((-1/2)x)

Are my answers right... help would be appreciated thank you

2. hELLO, rajr!

Find the general solution of the second order differential equation: . $4y''+ 8y' + 3y \:=\: 0$

Find the particular solution that satisfies the initial conditions: . $y(0) = 2$ and $y'(0) = 1$

I got the general solution to be: . $y(x) \:= C_1e^{-\frac{3}{2}x}+ C_2e^{-\frac{1}{2}x}$

and by intitial conditions, I got the particular solution to be: . $y(x) \:= \:-\tfrac{3}{2}e^{-\frac{3}{2}x} +\tfrac{7}{2}e^{-\frac{1}{2}x}$

Are my answers right? . . . . Absolutely!

Ya done real good!