Question

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.)
$\frac{dy}{dx}$ = 4x^1/6

Answer 1

Answer:

For this we can first multiply both sides by dx:

$dy = 4x^{1/6}dx$

Next we can integrate both sides:

$\int dy = \int 4x^{1/6}dx$

We can then solve both integrals to get:

$y = 4(\frac{6}{7}x^{\frac{7}{6}}+C_1) = \frac{24}{7}x^{\frac{7}{6}}+C_2$

We can just say the constant is C2. So the answer is

$y = \frac{24}{7}x^{\frac{7}{6}}+C_2$

We can also check this by differentiating both sides. We will ultimately get the equation we with. If I made any mistakes or misread something, please let me know.