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^(x)dot`

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 whose slope is given by (dy)/(dx)=(2y)/x ; x >0,\ y >0 and which passes through the point (1,1) is

Find the equation of the curve whose slope at x=0 is 3 and which passes through the point (0,1) satisfying the differential equation (x^2+1) (d^2y)/dx^2=2x dy/dx .

The slope of the curve y = x^(3) - 2x+1 at point x = 1 is equal to :

The equation of one of the curves whose slope of tangent at any point is equal to y+2x is (A) y=2(e^x+x-1) (B) y=2(e^x-x-1) (C) y=2(e^x-x+1) (D) y=2(e^x+x+1)

For the curve y=4x^3-2x^5, find all the points at which the tangent passes through the origin.

Equation of the diameter of the circle x^(2) +y^(2) - 2x + 4y = 0 which passes through the origin is

For the curve y=4x^3-2x^5 find all points at which the tangent passes through the origin.

For the curve y=4x^3-2x^5, find all the points at which the tangents pass through the origin.