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Chapter 1: Q6 E (page 14)

In Problems 3-8, determine whether the given function is a solution to the given differential equation.

x=cos2t,dxdt+tx=sin2t

Short Answer

Expert verified

The given function is not a solution to the given differential equation.

Step by step solution

01

Differentiating the given equation w.r.t. (with respect to) t.

Firstly, we will differentiate x=cos2twith respect to t,

dxdt=-2sin2t

02

Simplification.

Putting the values from step 1 in the L.H.S. (Left-hand side) of the given differential equation,

dxdt+tx=-2sin2t+tcos2t

which is not the same as the R.HS. (Right-hand side) of the given differential equation.

Hence,x=cos2tis not a solution to the differential equation dxdt+tx=sin2t.

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