Question

Solve the given differential equation by separation of variables. dN/dt + N = Nteᵗ + 7

Answer 1

To solve the given differential equation, separate the variables and then integrate both sides.

Step-by-step explanation:

To solve the given differential equation by separation of variables, we need to separate the variables and integrate both sides. Here are the steps:

1. Start with the equation: dN/dt + N = Nteᵗ + 7
2. Separate the variables by moving all the terms involving N to one side and terms involving t to the other side: dN/(N - Nteᵗ - 7)= dt
3. Integrate both sides: ∫dN/(N - Nteᵗ - 7) = ∫dt
4. After integration, solve for N to obtain the solution to the differential equation.