Question

Find the solution of the differential equation dy/dx = 3xe^y, that satisfies the given initial condition y(0) = 0.

a) y = ln(3x + 1)
b) y = ln(3x - 1)
c) y = ln(3x)
d) y = ln(x + 1)

Answer 1

To find the solution of the differential equation dy/dx = 3xe^y, separate the variables, integrate, and apply the initial condition to find the solution y = ln(3x + 1).

Step-by-step explanation:

To find the solution of the differential equation dy/dx = 3xe^y

Separate the variables by moving all the terms involving y to one side and all the terms involving x to the other side.

1. Integrate both sides of the equation with respect to x.
2. Apply the initial condition y(0) = 0 to find the constant of integration.
3. Simplify the equation to find the solution.

The solution to the differential equation dy/dx = 3xe^y with the initial condition y(0) = 0 is y = ln(3x + 1).