Question

Method of solving homogeneous differential equation

Answer 1

Answer:

first order Differential Equation is Homogeneous when 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 Different

Answer 2

Answer:

Step-by-step explanation:

1 take y=vx hence we get dy/dx =v+xdv/dx

2 find xdy/dx  by substiuting the above

3 seprate the varibales in x and v and integrate

4 replace v by y/x

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