Thread: Linear Differential Equations

Hello, I'd appreciate some help finding the general solution of the differential equation:

\frac{d^2 y}{dx^2} + 4y = \sin{x}

a^2 + 4a =0
(a + 2)^2 = 4
a = 0, a = 4

y = Ce^4x + B

But how do I find the particular integral?

Edit: Sorry it's been a while since I've Latex'd, and I'm kinda in a hurry, so I'll leave it as it is.

Originally Posted by Nyoxis

Hello, I'd appreciate some help finding the general solution of the differential equation:

\frac{d^2 y}{dx^2} + 4y = \sin{x}

a^2 + 4a =0
(a + 2)^2 = 4
a = 0, a = 4

y = Ce^4x + B

But how do I find the particular integral?

Edit: Sorry it's been a while since I've Latex'd, and I'm kinda in a hurry, so I'll leave it as it is.

Hi

First the characteristic equation is which leads to



The particular solution can be found as

leads to