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Chapter 4: Q23E (page 164)

In Problems 22鈥�25, use the method described in Problem 21 to find a general solution to the given equation.

23. 5Y' + 4Y = 0

Short Answer

Expert verified

The general solution is y(t)=ce-45t.

Step by step solution

01

Substitute y = ert

The given differential equation is 5y' + 4y = 0

Substitute y = ert and y' = rert,

5(rert)+4(ert)=0(5r+4)(ert)=05r+4=0

Therefore,

r=-45

02

Find the general solution.

Thus, the general solution is y(t)=ce-45t.

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Most popular questions from this chapter

The auxiliary equation for the given differential equation has complex roots. Find a general solution.w''+4w'+6w=0

Find a particular solution to the differential equation.

2z''+z=9e2t

Determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) y''-6y'+9y=5t6e3t

Find a particular solution to the differential equation.

y''+2y'-y=10

Find a general solution.y'''-y''+2y=0
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