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Chapter 4: Q12E (page 164)

Question: Find a general solution to the given differential equation.

3y''+11y'-7y=0

Short Answer

Expert verified

Answer

The general solution of the given equation isy=c1e-11+2056t+c2e-11-2056t.

Step by step solution

01

Firstly, write the auxiliary equation of the given differential equation.

The given differential equation is3y''+11y'-7y=0.

The auxiliary equation for the above equation3m2+11m-7=0.

02

Now find the roots of the auxiliary equation.

Solve the auxiliary equation,

3m2+11m-7=0m=-11±112-43-723m=-11±121+846m=-11±2056

The roots of the auxiliary equation are

m1=-11+2056, & m2=-11-2056.

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 isy=c1e-11+2056t+c2e-11-2056t.

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Most popular questions from this chapter

Determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y''-y'-12y=2t6e-3t

Solve the given initial value problem.y''+9y=0;y(0)=1,y'(0)=1

Using the mass-spring analogy, predict the behavior as t→∞of the solution to the given initial value problem. Then confirm your prediction by actually solving the problem.

(a). y''+16y=0;y(0)=2,y'(0)=0(b). y''+100y'+y=0;y(0)=1,y'(0)=0(c). y''-6y'+8y=0;y(0)=1,y'(0)=0(d). y''+2y'-3y=0;y(0)=-2,y'(0)=0(e). y''-y'-6y=0;y(0)=1,y'(0)=1

Find a particular solution to the differential equation.

y''+4y=8sin(2t)

Find a general solution z"+10z'+25z=0
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