Question

Find the explicit general solution to the following differential equation.

Answer 1

Answer:

y = (8+x)^5 + C

Step-by-step explanation:

Given the differential equation

(8+x) dy/dx = 5y

Using the variable separable method

(8+x) dy = 5ydx

dx/8+x = dy/5y

Integrate both sides

$\int\limits^ {} \, \frac{dx}{8+x} = \int\limits^ {} \, \frac{dy}{5y} \\ln(8+x) = \frac{1}{5}lny\\5ln(8+x)= lny\\ln(8+x)^5 = lny\\ (8+x)^5 = y\\Swap\\y = (8+x)^5 + C$

This gives the required solution