Solve the differential equation using separation of variables. $\frac { d y } { d x } = x y + 6 y + 2 x + 12$
A) $y = \frac { x ^ { 2 } y } { 2 } + \frac { 6 y ^ { 2 } } { 2 } + \frac { 2 x ^ { 2 } } { 2 } + 12 x + C$
B) $y = x y ^ { 2 } - 2 x ^ { 2 } + C$
C) $x = 5 , y = 0$
D) $y = C e ^ { \frac { x ^ { 2 } } { 2 } 6 x } - 2$

Question

Quizplus · Accepted Answer

The differential equation can be rewritten as $\frac{dy}{dx} = y(x + 6) + 2(x + 6)$. By separating variables and integrating, we find $y = Ce^{\frac{x^2}{2} + 6x} - 2$.

Solve the Differential Equation Using Separation of Variables dydx=xy+6y+2x+12\frac { d y } { d x } = x y + 6 y + 2 x + 12dxdy​=xy+6y+2x+12

Solve the Differential Equation Using Separation of Variables $\frac { d y } { d x } = x y + 6 y + 2 x + 12$