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Chapter 4: Q4.3-18E (page 172)

Find a general solution.2y"+13y'-7y=0

Short Answer

Expert verified

The general solution of the given equation2y"+13y'-7y=0isrole="math" localid="1654072917909" y(t)=c1e12t+c2e-7t.

Step by step solution

01

Differentiate the value of y.

Given differential equation is 2y"+13y'-7y=0.

Let y=eit.

Therefore,

y'(t)=retty''(t)=r2ert

02

Finding the roots of the auxiliary equation.

Then the auxiliary equation is 2r2+13r-7=0.

Solve the equation to obtain the roots of the auxiliary equation.

r=-13卤132-4脳2脳-72脳2r=-13卤169+564r=-13卤2254r=-13卤154r=12鈥塷谤鈥�r=-7

03

Final answer.

Therefore, the general solution isy(t)=c1e12t+c2e-7t .

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