If the slope of the tangent to the curve at any point P (x, y) is y x - ² y x , then the equation of a curve passing through (1, 4 ) is

Step-by-step solution

According to the condition, dy dx = y x - ² y x (i) This is a homogeneous differential equation Substituting y=v x , we get array l v+x dv dx =v- ² v x dv dx =- ² v ² vdv =- dx x v=- x+ C y x + x= C array Substituting x =1, y= 4 , we get C =1 Thus, we get ( y x )+ x=1 which is the required solution.