MAT136H1 Lecture Notes - Product Rule, Integrating Factor
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9.5 Differential Equations
Question #4 (Medium): Solving the Initial Value for the Linear Differential Equation
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.
Solve the initial value problem.
First the equation need to be arranged in the form of linear differential equation:
. 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
The equation can be divided by the integrating factor:
Now since , plug into the equation and to find the missing value :
Therefore the solution to the initial value problem is
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