Question

Find the solution for differential equation using appropriate technique: d y/d x + y^2 +y+1/x^2+x+1=0

Answer 1

Answer:

hen it can be in this form:

dydx = F( yx )

We can solve it using Separation of Variables but first we create a new variable v = y x

v = yx which is also y = vx

And dydx = d (vx)dx = v dxdx + x dvdx (by the Product Rule)

Which can be simplified to dydx = v + x dvdx

Using y = vx and dydx = v + x dvdx we can solve the Differential Equation.

An example will show how it is all done:

Example: Solve dydx =