For a first order linear equation in the form y\'+p(x)y=f(x) the general solutio

Question

For a first order linear equation in the form y'+p(x)y=f(x) the general solution is obtained by finding an integrating factor u(x)=exp (intergalp(x)dx ) The general solution is a sum of two parts y=yc+yp where yc is the general solution of the homogeneous problem yc(x)=Cu(x)^?1=Cexp(?p(x)dx) where C is an arbitrary constant and yp is a particular solution of the non-homogeneous problem yp(x)=u(x)^?1intergal u(x)f(x)dx Consider the equation 3y'+12y=6 (A) Find the integrating factor u(x) u(x)= (B) Find the general solution of the homogeneous problem yc(x). Note use C for the arbitrary constant. yc(x)= (C) Find the particular solution yp(x) yp(x)= (D) Find the general solution y=yc+yp. Note use C for the arbitrary constant. y(x)=

Explanation / Answer

A) e^12x

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