Porisma

A hint to get started

Solve a homogeneous first-order differential equation

Use u=y/xu=y/x to show that dydx=y2+xy+x2x2\dfrac{dy}{dx}=\dfrac{y^2+xy+x^2}{x^2}, x>0x>0, reduces to 1u2+1dudx=1x\dfrac1{u^2+1}\dfrac{du}{dx}=\dfrac1x. Hence find yy in terms of xx.

[2017/NJC/I/10(a)]

CJC · Discussion · Question 4

Treat u as a function of x when differentiating y = ux.

Read the worked solution