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Chapter 4: Q16E (page 164)

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

y"-4y'-5y = 0 : y(-1) = 3,y'(-1) = 9

Short Answer

Expert verified

The solution is y(t)=-23et-1+53e5+5t.

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;

r2-4r1-53t0=0r2-4r-5=0r2+r-5r-5=0r(r+1)-5(r+1)=0(r+1)(r-5)=0r=-1,5

Therefore, the solution is y(t) = c1e-t + c2e5t.

02

Apply initial conditions.

The initial conditions are y(-1) = 3,y'(-1) = 9.

Therefore,

y(-1)=c1e1+c2e-5c1e1+c2e-5=3

And

y'(t)=-c1e-t+5c2e5ty'(-1)=-c1e1+5c2e-5-c1e1+5c2e-5=9

Solving for c1,c2 then,

c1=-23e-1c2=53e5

Therefore, the solution is y(t)=-23et-1+53e5+5t.

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Most popular questions from this chapter

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