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Chapter 1: Q4 E (page 13)

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

x=2cost-3sint鈥�,鈥�鈥�鈥�x''+x=0

Short Answer

Expert verified

The given function is a solution to the given differential equation.

Step by step solution

01

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

Firstly, we will differentiate x=2cost-3sint鈥�with respect to t,

x'=-2sint-3cost

Again, differentiating with respect to t,

x''=-2cost-3-sintx''=-2cost+3sint

02

Simplification

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

x''+x=-2cost+3sint+2cost-3sintx''+x=0

which is the same as the R.HS. (Right-hand side) of the given differential equation.

Hence, x=2cost-3sint鈥�is a solution to the differential equation x''+x=0.

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