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Differential Equations/Maths2
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Question
solve the initial vale second order homogeneous linear differential equation:
y"-4y'+4y=0 ,y(0)=0,y'(o)=-3,
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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Differential Equations
Answers by Expert:
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
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