Question

Use the separation method to solve the initial value problem

differential equation, express the solution explicitly as a
function of the independent value.
dy/dx = 5x + 15, y(1)=1

Answer 1

To solve the initial value problem dy/dx = 5x + 15, we can use the separation of variables method.

Step-by-step explanation:

To solve the initial value problem, we can use the separation of variables method. We start by separating the variables, which gives us:

dy/dx = 5x + 15

Next, we integrate both sides of the equation with respect to y and x separately:

∫ dy = ∫ (5x + 15) dx

Integrating both sides gives:

y = 2.5x^2 + 15x + C

To find the value of C, we can use the initial condition y(1) = 1. Substituting this into the equation:

1 = 2.5(1)^2 + 15(1) + C

Simplifying the equation gives:

C = -16.5

Therefore, the solution to the initial value problem is:

y = 2.5x^2 + 15x - 16.5.