Solve the initial value problem using an integrating factor.
-$y ^ { \prime }$ + y = 3; y(0) = 0.
A) y = $e ^ { - t }$ (3t - $e ^ { - t }$ )
B) y = $\sqrt { 6 t }$
C) y = 3 - 3 $e ^ { - t }$
D) y = 3t

Question

Solve the initial value problem using an integrating factor. 
-$y ^ { \prime }$ + y = 3; y(0) = 0.
A) y = $e ^ { - t }$ (3t - $e ^ { - t }$ )
B) y = $\sqrt { 6 t }$
C) y = 3 - 3 $e ^ { - t }$
D) y = 3t

Quizplus · Accepted Answer

The integrating factor is $e^t$, multiplying both sides by this gives $e^t y' + e^t y = 3e^t$. This simplifies to $(e^t y)' = 3e^t$, integrating both sides with respect to $t$ gives $e^t y = 3e^t + C$. Using the initial condition $y(0) = 0$, we find $C = -3$. Thus, $y = 3 - 3e^{-t}$.

Solve the Initial Value Problem Using an Integrating Factor y′y ^ { \prime }y′

Solve the Initial Value Problem Using an Integrating Factor $y ^ { \prime }$