Find the general solution of $\frac { d y } { d x } = x ^ { 3 } + 9$ .
A)y = 9x + C
B) $y = 4 x ^ { 4 } + 9 x + C$
C) $y = 3 x ^ { 2 } + C$
D) $y = \frac { x ^ { 4 } } { 4 } + 9 x + C$

Question

Quizplus · Accepted Answer

To find the general solution of the differential equation $\frac { d y } { d x } = x ^ { 3 } + 9$, we integrate the right-hand side with respect to $x$. The integral of $x^3$ is $\frac{x^4}{4}$ and the integral of $9$ is $9x$. Therefore, the general solution is $y = \frac{x^4}{4} + 9x + C$, where $C$ is the constant of integration.

Find the General Solution Of dydx=x3+9\frac { d y } { d x } = x ^ { 3 } + 9dxdy​=x3+9

Find the General Solution Of $\frac { d y } { d x } = x ^ { 3 } + 9$