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Chapter 5: Q1E (page 259)

In Problems 1鈥�7, convert the given initial value problem into an initial value problem for a system in normal form.

y''(t)+ty'(t)-3y(t)=t2;y(0)=3,y'(0)=-6

Short Answer

Expert verified

x'1(t)=x2(t)x'2(t)=-tx2+3x1+t2x1(0)=3x2(0)=-6

Step by step solution

01

Express the equation in form of x.

Here given;

y''(t)+ty'(t)-3y(t)=t2

Denote,

x1(t)=y(t)x2(t)=y'(t)

The equation transforms as;

x'1(t)=x2(t)x'2(t)=-tx2+3x1+t2

02

the initial conditions

The given initial conditions arey(0)=3,y'(0)=-6

Initial conditions after transformations;

x1(0)=3x2(0)=-6

This is the required result.

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Most popular questions from this chapter

Suppose the displacement functions xtandyt for a coupled mass-spring system (similar to the one discussed in Problem 6) satisfy the initial value problem

x''(t)+5x(t)-2y(t)=0y''(t)+2y(t)-2x(t)=3sin2tx(0)=x'(0)=0y(0)=1,y'(0)=0

Solve forxt andyt

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