Question

If 2y= X(1+dy/dx) show that y2 is constant

Answer 1

Answer:

y''=2C

Step-by-step explanation:

The equation can be expressed as dy/dx - (2/x)y=-1 and this has an integrating

factor e^(integral -2/x dx) =e^(-2ln(*x)=1/x^2 and multiplying the DE by this gives

((1/x^2)y)'= -1/x^2 and integrating gives (1/x^2)y=1/x + C giving

y=x+Cx^2 and y'=1+2Cx and y"=2C which is a constant.