Author Topic: TUT0702 Quiz3  (Read 3975 times)

Qihui Huang

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TUT0702 Quiz3
« on: October 11, 2019, 02:26:03 PM »
Verify that the functions y1 and y2 are solutions of the given differential equation. Do they constitute a fundamental set of solutions?

$$y''-2y+y=0,y_1(t)=e^t, y_2(t)=te^t$$

Differentiate $y_1(t)=e^t, y_2(t)=te^t$ respect to t,
$$y_1'=e^t, y_2'=e^t+te^t$$
Substitute back to the differential equation,
So both $y_1(t)$ and $y_2(t)$ are two valid solutions to the equation.

To check whether it is a fundamental set of solution:
We want  $W(y_1,y_2)(t) \neq 0$
The determinant is not zero, so it is a fundamental set of solutions.
« Last Edit: October 11, 2019, 02:28:53 PM by Qihui Huang »