Find the equation of a curve passing through the point (0, 0) and whose differential equation is `y' = e^x sinx`

Find the equation of the curve passing through the point (1, 1) whose differential equation is xcdotdy = (2x^2 + 1)cdotdx(xne0)

Find the equation of the curve passing through the point (0,pi/4) whose differential equation is sinx cosy dx + cosx siny dy = 0

Find the equation of a curve passing through the origin and satisfying the differential equation (1+x^2)(dy)/(dx)+2xy=4x^2

Find the equation of a line passing through the point (0,1) and parallel to : 3x-2y+5 = 0 .

Find the equation ofthe circle passing through the points (2,3) and (-1,1) and whose centre is on the line x-3y- 11 =0 .

Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

Find the equation of the plane passing through the points (0,-1,0),(1,1,1) and (3,3,0).