If a curve passes through the point 1 ,   - 2 and has slope of the tangent at any point x ,   y on it as x 2 - 2 y x , then the curve also passes through the point

Question

If a curve passes through the point 1 , &#160; - 2 and has slope of the tangent at any point x , &#160; y on it as x 2 - 2 y x , then the curve also passes through the point

Aicharya · Accepted Answer

d y d x = x 2 - 2 y x &#8658; d y d x + 2 x y = x . It is in linear form. I.F. = e &#8747; 2 x d x = e 2 l n x = x 2 &#8756; y . x 2 = &#8747; x . x 2 &#160; d x = x 4 4 + c &#8757; At x = 1 , &#160; y = - 2 , &#8756; - 2 &#215; 1 2 = 1 4 4 + c &#8658; c = - 2 - 1 4 = - 9 4 &#8756; curve is y . x 2 = x 4 4 - 9 4 &#8756; It passes through 3 , &#160; 0 .

If a curve passes through the point 1 ,   - 2 and has slope of the tangent at any point x ,   y on…

Solution

If a curve passes through the point 1 , &#160; - 2 and has slope of the tangent at any point x , &#160; y on…

Solution

If a curve passes through the point 1 , - 2 and has slope of the tangent at any point x , y on…