Find the general solution of the following differential

zatajuxoqj

zatajuxoqj

Answered question

2022-03-22

Find the general solution of the following differential equation (where primes denote derivatives with respect to x):
y+8y+16=0

Answer & Explanation

Cassius Villarreal

Cassius Villarreal

Beginner2022-03-23Added 11 answers

Given the differential equation,
y+8y+16=0
It is a second order linear homogeneous equation.
Auxiliary equation of the above equation is m2+8m+16=0
Solving the auxiliary equation,
m2+8m+16=0
m2+4m+4m+16=0
m(m+4)+4(m+4)=0
(m+4)2
Hence the roots are same. That is m=4
So, the solution of y+8y+16=0 is,
y=(c1+c2)e4t where c1 and c2 constants
Jeffrey Jordon

Jeffrey Jordon

Expert2022-03-31Added 2605 answers

Answer is given below (on video)

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