Final answer:
To solve the given differential equation, we need to separate the variables and integrate both sides. Follow the provided steps to obtain the solution.
Step-by-step explanation:
To solve the given differential equation, we need to separate the variables and integrate both sides. Here's how:
We start by multiplying both sides of the equation by (x+7) to eliminate the denominator:
(x+7)y' + 3y = (x+7)^2
Next, we rearrange the equation to separate the variables:
(x+7)y' = (x+7)^2 - 3y
Now, we integrate both sides with respect to x:
∫(x+7)y' dx = ∫[(x+7)^2 - 3y] dx
Integrating the left side gives us: y = ∫[(x+7)^2 - 3y] / (x+7) dx
And integrating the right side gives us: y = ∫[(x+7)^2 - 3y] dx
Now, we can solve the integral to find the solution to the differential equation.