Question

Find the general solution of
dy/dx + 2y =6​

Answer 1

ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C

Explanation:

dy/dx + 2y = 6

This is a first order linear ODE.

p(x) = 2

Integrating factor: I(x) = e^(∫ 2 dx) = e^(2x)

e^(2x)(dy/dx + 2y) = 6e^(2x)

e^(2x) dy + 2ye^(2x) dx = 6e^(2x) dx

Integrate both sides of the equation.

ye^(2x) = 3e^(2x) + C

Thus, the general solution is ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C.