The solution of the initial value problem $y ^ { \prime } = 3 y , y ( 0 ) = 2$ is $y = c e ^ { 3 x }$ , where $c =$
A) 2
B) $- 2$
C) 3
D) $- 3$
E) 1

Question

Quizplus · Accepted Answer

To find the constant $c$, we substitute the initial condition $y(0) = 2$ into the solution $y = c e^{3x}$. Setting $x = 0$, we get $y(0) = c e^{3 \cdot 0} = c e^{0} = c$. Since $y(0) = 2$, it follows that $c = 2$.

The Solution of the Initial Value Problem y′=3y,y(0)=2y ^ { \prime } = 3 y , y ( 0 ) = 2y′=3y,y(0)=2

The Solution of the Initial Value Problem $y ^ { \prime } = 3 y , y ( 0 ) = 2$