The solution of the initial value problem $y ^ { \prime } = 5 y , y ( 1 ) = 3$ is $y = c e ^ { 5 x }$ , where $c =$
A) $3 e ^ { - 5 }$
B) 3
C) $3 e ^ { 5 }$
D) $- 3 e ^ { 5 }$
E) $- 3$

Question

Quizplus · Accepted Answer

To find the constant $c$, substitute $x = 1$ and $y = 3$ into the solution $y = c e^{5x}$. This gives $3 = c e^{5}$. Solving for $c$ gives $c = 3e^{-5}$.

The Solution of the Initial Value Problem y′=5y,y(1)=3y ^ { \prime } = 5 y , y ( 1 ) = 3y′=5y,y(1)=3

The Solution of the Initial Value Problem $y ^ { \prime } = 5 y , y ( 1 ) = 3$