The solution of the initial value problem $y ^ { \prime } = 2 y + x , y ( 1 ) = 1 / 4$ is $y = - x / 2 - 1 / 4 + c e ^ { 2 x }$ , where $c =$
A) 2
B) $e ^ { - 2 }$
C) $e ^ { - 1 }$
D) $e ^ { - 2 } / 2$
E) 1

Question

Quizplus · Accepted Answer

To find the value of $c$, we substitute the initial conditions $x = 1$ and $y = 1/4$ into the solution. This gives us $1/4 = -1/2 - 1/4 + c e^{2}$. Solving for $c$, we find $c = e^{-2}$.

The Solution of the Initial Value Problem y′=2y+x,y(1)=1/4y ^ { \prime } = 2 y + x , y ( 1 ) = 1 / 4y′=2y+x,y(1)=1/4

The Solution of the Initial Value Problem $y ^ { \prime } = 2 y + x , y ( 1 ) = 1 / 4$