Using the method of variation of parameters, solve the following inhomogeneous equation. y′′+12y′+36y=(−1e −6x )/(x 2 +1) a) Write the characteristic equation of the homogeneous part of the equation...

Using the method of variation of parameters, solve the following inhomogeneous equation.

y′′+12y′+36y=(−1e^−6x)/(x²+1)

a) Write the characteristic equation of the homogeneous part of the equation using the variable m.

....?....=0

b) Write down the homogeneous solution of the equation. Denote the constants c₁
and c₂
with c₁
and c₂. The y₁
and y₂
solutions must satisfy the conditions y₁(0)=1, y₂(0)=0, respectively.

y_h=?

c) Find Wronskian: W(y1,y2)=?

d) W1=?

e) W2=?

f) u′1=? u1=?

g)u′2=? u2=?

h) Write down the specific solution you got: yp=?

e) Write down the general solution of the equation: y=?