QuestionFind the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.) $$\begin{array}{r} \frac{d y}{d x}=2 x^{3 / 7} \\ y=\square \end{array}$$

Studdy Solution
Verify the solution by differentiating it with respect to $x$:
Differentiate $y = \frac{7}{5} x^{10/7} + C$:
$$\frac{dy}{dx} = \frac{7}{5} \cdot \frac{10}{7} x^{10/7 - 1}$$
$$\frac{dy}{dx} = 2 x^{3/7}$$
Since the derivative matches the original differential equation, the solution is verified.
The general solution is:
$$y = \frac{7}{5} x^{10/7} + C$$