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Chapter 4: Q15E (page 164)

In Problems 13鈥�20, solve the given initial value problem.

y"-4y'+3y=0:y(0)=1,y'(0)=13

Short Answer

Expert verified

The solution is y(t)=43et-13e3t.

Step by step solution

01

Find the solution of the differential equation.

The given differential equation is. y" - 4y' + 3y = 0

The auxiliary equation is;

r2-4r1+3r0=0r2-4r+3=0r2-r-3r+3=0r-1r-3=0r=1,3

Therefore, the solution is y(t) = c1et + c2e3t.

02

Apply initial conditions.

The initial conditions arey(0)=1,y'(0)=13

Therefore,

y(0)=c1e0+c2e0c1+c2=1

And

y'(t)=c1et+3c2e3ty'(0)=c1e0+3c2e0c1+3c2=13

Solving for c1,c2 then;

c1=43c2=-13

Therefore, the solution is y(t)=43et-13e3t.

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