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

Question

Quizplus · Accepted Answer

To find the general solution, we integrate both sides with respect to $x$:
$$\int \frac{dy}{dx} dx = \int (2x^2+5x)dx$$
$$y = \frac{2}{3}x^3+\frac{5}{2}x+C$$
Therefore, the correct answer is D.

Use Integration to Find a General Solution of the Differential dydx=2x2+5x\frac { d y } { d x } = 2 x ^ { 2 } + 5 xdxdy​=2x2+5x

Use Integration to Find a General Solution of the Differential $\frac { d y } { d x } = 2 x ^ { 2 } + 5 x$