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Chapter 4: Q8RP (page 231)

Find a general solution to the given differential equation.25y''+20y'+4y=0

Short Answer

Expert verified

The general solution to the given differential equation isy=c1e-25t+c2te-25t.

Step by step solution

01

Write the auxiliary equation of the given differential equation

The given differential equation is25y''+20y'+4y=0.

The auxiliary equation for the above equation25m2+20m+4=0.

02

Find the roots of the auxiliary equation. 

Solve the auxiliary equation,

25m2+20m+4=05m+22=0

The roots of the auxiliary equation arem1=-25,鈥夆赌�&鈥夆赌�m2=-25.

Thus, the general solution of the given equation isrole="math" y=c1e-25t+c2te-25t.

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Most popular questions from this chapter

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