Solve the differential equation. (Use C for any needed constant.) \\ 4\frac{dy}{d\theta} = \frac...

Question:

Integration using by parts and variable separable methods

To solve the given integral equation we have to use integration by parts method and variable separable method.

Integration by parts .

Let u and {eq}v^{\prime} {/eq} be two functions in t then

{eq}\int u v^{\prime} dt = u v - \int u ^{\prime} v dt + C {/eq}

Variable separable method.

If the differential equation is in the form {eq}\frac { dy}{dx } = F(x) \ G(y) {/eq} Where F and G are functions in x and y respectively .

Then we can convert the given d.e in the form {eq}\frac { dy}{G(y) } = F(x) \ dx \\ => \int \frac { dy}{G(y) } = \int F(x) \ dx {/eq}.

Answer and Explanation: 1