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About Abe 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.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

 
   

You are here:  Experts > Science > Mathematics > Differential Equations > Maths2

Differential Equations - Maths2


Expert: Abe Mantell - 5/31/2009

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

Final answer: y(x)=3xe^(2x)

Abe


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