Question

Find a particular solution of y"+y=2e^x

Answer 1

Use the annihilator method on the 2e^x. Think, what differential operator would result in the answer.

Answer 2

is there a formula i can follow? this is supposed to be a non homogeneous second order differential equation.

Answer 3

Well, you need to use the differential operator concept. What D would destroy 2e^x? Then use that differential operator and create the particular solution. Then plug that solution into the function, and see what the coefficient is.

Answer 4

(e^x)"+(e^x)=2e^x

Answer 5

D-1 = Ae^(1x)
yp = Ae^(1x)
e^x = Ae^x+A^ex = 2e^x

Answer 6

sorry, function, not e^x

Answer 7

also, use t for 1.

Answer 8

I mangled that a little bit. Your y_p = Ae^x. You have to determine what A is. To do that, substitute the y_p back into the function, and solve for A.