Find the solution to the differential equation $\frac { d y } { d x } = x y$ satisfying $y ( 0 ) = 3$ .
A) $y = 3 + e ^ { x ^ { 2 } / 2 }$
B) $y = e ^ { 3 x ^ { 2 } / 2 }$
C) $y = 3 e ^ { x ^ { 2 } / 2 }$
D) $y = \frac { e ^ { x ^ { 2 } / 2 } } { 3 }$

Question

Quizplus · Accepted Answer

This differential equation is a first-order linear ordinary differential equation that can be solved using the method of separation of variables. The solution is $y = 3e^{x^2/2}$, which satisfies the initial condition $y(0) = 3$.

Find the Solution to the Differential Equation dydx=xy\frac { d y } { d x } = x ydxdy​=xy

Find the Solution to the Differential Equation $\frac { d y } { d x } = x y$