Let us consider a curve, y = f x passing through the point - 2 ,   2 and the slope of the tangent to the curve at any point ( x ,   f ( x ) ) is given by f ( x ) + x f ' ( x ) = x 2 . Then

Question

Let us consider a curve, y = f x passing through the point - 2 , &#160; 2 and the slope of the tangent to the curve at any point ( x , &#160; f ( x ) ) is given by f ( x ) + x f ' ( x ) = x 2 . Then

Aicharya · Accepted Answer

y + x d y d x = x 2 d y d x + y x = x I . F . = e &#8747; 1 x d x = x Solution of differential equation, y &#183; x = &#8747; x &#183; x &#160; d x x y = x 3 3 + C Passes through - 2 , &#160; 2 , So, - 12 = - 8 + 3 C C = - 4 3 &#8756; &#160; 3 x y = x 3 - 4 i.e 3 x &#183; f x = x 3 - 4 x 3 - 3 x &#160; f x - 4 = 0

Let us consider a curve, y = f x passing through the point - 2 , &#160; 2 and the slope of the tangent to…

Solution

Let us consider a curve, y = f x passing through the point - 2 , 2 and the slope of the tangent to…