The curve C has the equation ye ^(–2x) = 2x + y^2 . Find dy/dx in terms of x and y.
differentiate both side with respect to x : (dy/dx)e^(-2x)+y(-2e^(-2x)) = 2+2y(dy/dx)
rearrange it : (-2y+e^(-2x))(dy/dy) = 2 + 2ye^(-2x) ==> dy/dx = ( 2 + 2ye^(-2x) ) / ( -2y+e^(-2x) )
JC
Related Maths A Level answers
All answers ▸Integrate cos^2(x)
y(x) = x^2(1-x)e^-2x , find y'(x) in the form of g(x)e^-2x where g(x) is a cubic function to be found
Use logarithms to solve the equation 2^(n-3) = 18000, giving your answer correct to 3 significant figures.
Given that y=π/6 at x=0 solve the differential equation,dy/dx=(e^x)cosec2ycosecy