Thread: Differential equations - seperation of variables

Solve the given differential equation by Separation of variables.

(1+x^4)dy + x(1+4y^2)dx = 0, y(1)=0
(3x^2 + 9xy + 5y^2)dx – (6x^2 +4xy)dy = 0, y(2) = -6
(3y^2-x^2 / y^5)dy/dx + x/2y^4 = 0, y(1) = 1
Dr/dQ + rsecQ = cosQ

Originally Posted by wyasser

Solve the given differential equation by Separation of variables.

(1+x^4)dy + x(1+4y^2)dx = 0, y(1)=0
(3x^2 + 9xy + 5y^2)dx – (6x^2 +4xy)dy = 0, y(2) = -6
(3y^2-x^2 / y^5)dy/dx + x/2y^4 = 0, y(1) = 1
Dr/dQ + rsecQ = cosQ

It will help people to answer your question if you write out your equations using LATEX.

For the first one:



Here divide both sides by , this will leave you with:



Hint, for the x variable consider using partial fractions to simplify the equation before you try and integrate.

The second one is a little harder.



For this one I would suggest using a substitution to simplify the equation a little before you attempt to separate the variables.

Let where , if we differentiate this equation with respect to we get

.

Substitute in these 2 values and see how you go.

When you've done these try and see what you can manage with the last two.

Hope this helps