Determine whether the differential equation is linear. $y ^ { \prime } + 3 x ^ { 2 } y = 6 x ^ { 2 }$
A) the equation is linear
B) the equation is not linear

Question

Quizplus · Accepted Answer

The given differential equation is linear because it can be written in the standard form $y' + P(x)y = Q(x)$, where $P(x) = 3x^2$ and $Q(x) = 6x^2$. The equation involves the first derivative of $y$ and $y$ itself, both to the first power, with no products or nonlinear functions of $y$.

Determine Whether the Differential Equation Is Linear y′+3x2y=6x2y ^ { \prime } + 3 x ^ { 2 } y = 6 x ^ { 2 }y′+3x2y=6x2

Determine Whether the Differential Equation Is Linear $y ^ { \prime } + 3 x ^ { 2 } y = 6 x ^ { 2 }$