PLEASSEEEE HELPP By inspection find a particular solution of

PLEASSEEEE HELPP!!!!!!!

By inspection, find a particular solution of y\" + 2y - 10. Y_p(x) = By inspection, find a particular solution of y\" + 2y = -4x. y_p(x) = Find a particular solution of y\" + 2y = -4x + 10. Y_p(x) = Find a particular solution of y\" + 2y = 8x + 5.

Solution

a)

We have a constant function on the right and derivative of constant function is 0 so we can see y can be taken as constant function. We can see it must be

yp=5

b)

Second derivative of linear function is 0 so we can assume a function of the form: Ax+B as guess for particular solution. We can see it must be

yp=-2x

c)

We add solution from previous two parts since equation is linear

So,

yp=-2x+5

d)

We follow parts a,b,c

SOlution corresponding to 8x is 4x

And correspondg to 5 is 5/2

So, yp=4x+5/2