AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Question solve the initial vale second order homogeneous linear differential equation:
y"-4y'+4y=0 ,y(0)=0,y'(o)=-3,
Answer Let y=e^(rx), so we get the characteristic equation:
r^2-4r+4=0 ==> (r-2)(r-2)=0 ==> r=2,2
Repeated root, so the general solution is: y(x)=(A+Bx)e^(2x)
Now impose the IC's:
y(0)=0 ==> 0=(A+0)e^0 ==> A=0 ==> y(x)=Bxe^(2x)
y'(0)=3 ==> y'=Be^(2x)+2Bxe^(2x) ==> y'(0)=B, so B=3
