The solution to the differential equation $\frac { d y } { d x } = \frac { e ^ { x } } { 2 y }$ satisfying the boundary condition $y = 5$ when $x = 0$ is

A) $y ^ { 2 } = e ^ { x } + 3$
B) $y ^ { 2 } = e ^ { x } + 8$
C) $y ^ { 2 } = e ^ { x } + 15$
D) $y ^ { 2 } = e ^ { x } + 24$
E) $y ^ { 2 } = e ^ { x } + 35$

Question

The solution to the differential equation $\frac { d y } { d x } = \frac { e ^ { x } } { 2 y }$ satisfying the boundary condition $y = 5$ when $x = 0$ is

A) $y ^ { 2 } = e ^ { x } + 3$
B) $y ^ { 2 } = e ^ { x } + 8$
C) $y ^ { 2 } = e ^ { x } + 15$
D) $y ^ { 2 } = e ^ { x } + 24$
E) $y ^ { 2 } = e ^ { x } + 35$

Quizplus · Accepted Answer

To solve the differential equation, separate variables and integrate: $2y \, dy = e^x \, dx$. Integrating both sides gives $y^2 = e^x + C$. Applying the boundary condition $y = 5$ when $x = 0$, we find $25 = 1 + C$, so $C = 24$. Thus, the solution is $y^2 = e^x + 24$.

The Solution to the Differential Equation dydx=ex2y\frac { d y } { d x } = \frac { e ^ { x } } { 2 y }dxdy​=2yex​

The Solution to the Differential Equation $\frac { d y } { d x } = \frac { e ^ { x } } { 2 y }$