-x(1+x^(2))(dy)/(dx)=y(1-x^(2))+x^(3)log x

x(x^(2)+1)(dy)/(dx)=y(1-x^(2))+x^(3)*ln x

The solution of the differential equation x(x^(2)+1)((dy)/(dx))=y(1-x^(2))+x^(3)log x is

Solve x(x^(2)+1)(dy)/(dx)=y(1-x^(2))+x^(2)ln x

(dy)/(dx)-x sin^(2)x=(1)/(x log x)

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

If y=log(x+sqrt(1+x^(2))), then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=log (x + sqrt(x^(2) + 1)) then show that, (x^(2) + 1) (d^(2)y)/(dx^(2)) + x (dy)/(dx)= 0

If x^(x)+y^(x)=1, prove that (dy)/(dx)=-{(x^(x)(1+log x)+y^(x)log y)/(xy^((x-1)))}

Q.if log y=sin^(-1)x, show that,(1-x^(2))((d^(2)y)/(dx^(2)))=x((dy)/(dx))+y

If x^(logy)=logx , prove that, (x)/(y).(dy)/(dx)=(1-logx log y)/((log x)^(2))