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Chapter 4: Q10E (page 164)

Question: find a general solution to the given differential equation y''-y'-11y=0.

Short Answer

Expert verified

Answer

The general solution of the given equation isy=c1e1+352t+c2e1-352t.

Step by step solution

01

Write the auxiliary equation of the given differential equation.

The given differential equation isy''-y'-11y=0.

The auxiliary equation for the above equationm2-m-11=0.

02

Now find the roots of the auxiliary equation.

Solve the auxiliary equation,

m2-m-11=0m=--1卤1-41-112m=1卤452m=1卤352

The roots of the auxiliary equation are

m1=1+352,鈥�&鈥�m2=1-352.

03

Write the general solution.

If an auxiliary equation has distinct real roots&, then the general solution is given as;

y=c1em1t+c2em2t

Thus, the general solution of the given equation is

y=c1e1+352t+c2e1-352t.

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