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**preview**shows half of the first page. to view the full**1 pages of the document.**9.5 Differential Equations

Linear Equations

Question #4 (Medium): Solving the Initial Value for the Linear Differential Equation

Strategy

Solving initial value means once the linear differential equation has been solved, given the x and y value

combination, the arbitrary constant factor can be determined by working out the equation backward.

Sample Question

Solve the initial value problem.

, ,

Solution

First the equation need to be arranged in the form of linear differential equation:

Then

. The integrating factor is:

Multiply the integrating factor to the linear differential equation on both sides:

;

; the left side is then in the form of product rule:

; then integrate

both sides:

The equation can be divided by the integrating factor:

Now since , plug into the equation and to find the missing value :

;

; then

Therefore the solution to the initial value problem is

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