Use integration to find a general solution of the differential equation.
$\frac { d y } { d x } = 5 x ^ { 3 } + x$
A) $y = 5 x ^ { 4 } + x ^ { 2 } + C$
B) $y = \frac { 5 } { 4 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 2 } + C$
C) $y = 5 x ^ { 2 } + 1 + C$
D) $y = 15 x ^ { 2 } + 1 + C$
E) $y = \frac { 5 } { 4 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 2 } + x + C$

Question

Use integration to find a general solution of the differential equation. 
$\frac { d y } { d x } = 5 x ^ { 3 } + x$
A) $y = 5 x ^ { 4 } + x ^ { 2 } + C$
B) $y = \frac { 5 } { 4 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 2 } + C$
C) $y = 5 x ^ { 2 } + 1 + C$
D) $y = 15 x ^ { 2 } + 1 + C$
E) $y = \frac { 5 } { 4 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 2 } + x + C$

Quizplus · Accepted Answer

We have:
$$\frac { dy } { dx } = 5 x ^ { 3 } + x$$
Integrating both sides with respect to $x$ yields
$$y=\int\left(5x^3+x\right)dx=\frac{5}{4}x^4+\frac{1}{2}x^2+C$$
Therefore, the solution is $y=\frac{5}{4}x^4+\frac{1}{2}x^2+C$ where $C$ is the constant of integration.

Use Integration to Find a General Solution of the Differential dydx=5x3+x\frac { d y } { d x } = 5 x ^ { 3 } + xdxdy​=5x3+x

Use Integration to Find a General Solution of the Differential $\frac { d y } { d x } = 5 x ^ { 3 } + x$