Question

Find the general solution of the differential equation? y dy/dx=6cos x

Answer 1

`y=+-sqrt(12sinx+C)`

Explanation:

This is a separable equation. We'll keep all `y, dy` on the left side and all `x, dx` on the right side.

Then,

`ydy=6cosxdx`

Integrate both sides:

`intydy=int6cosxdx`

`1/2y^2=6sinx+C`

We would technically have two constants of integration; however, they have all been absorbed into the constant on the right.

We still need an explicit solution:

`y^2=12sinx+C`

Multiplying the constant by a constant doesn't change anything, so we won't change how we represent it.

`y=+-sqrt(12sinx+C)`