Show that the equation of the curve whose slope at any point is equal to `y+2x` and which passes through the origin is `y+2(x+1)=2e^(2x)dot`

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y = 2(e^(x) - x-1) .

What is the equation of the curve whose slope any point is equal to 2x and which passes through the origin?

The equation of one of the curves whose slope at any point is equal to y+2x and y(0)=0 is

Prove that the equation of a curve whose slope at (x,y) is -(x+y)/x and which passes through the point (2,1) is x^2+2xy=8

Find the equation of the curve whose gradient at (x,y) is y/(2x) and which passes through the point (a,2a) .

The equation of the curve,slope of whose tangent at any point (h,k) is (2k)/(h) and which passes through the point (1,1) is (i)x^(2)=y( ii) y^(2)=x( iii) x^(2)=2y( iv )y^(2)=2x

The slope of the tangent to the curve at any point is equal to y + 2x. Find the equation of the curve passing through the origin .