The solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ is
A) $y = c e ^ { x ^ { 2 } }$
B) $y = c e ^ { x ^ { 3 } }$
C) $y = c + e ^ { x ^ { 2 } }$
D) $y = c e ^ { x ^ { 3 } / 3 }$
E) $y = c + e ^ { x ^ { 3 } / 3 }$

Question

Quizplus · Accepted Answer

This differential equation is a first-order linear differential equation that can be solved using the method of separation of variables. By separating the variables and integrating both sides, we get $y = c e^{x^3/3}$, where $c$ is the integration constant.

The Solution of the Differential Equation y′=x2yy ^ { \prime } = x ^ { 2 } yy′=x2y

The Solution of the Differential Equation $y ^ { \prime } = x ^ { 2 } y$