`y^2+x^2(dy)/(dx)=x y(dy)/(dx)`

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^2 y(dy)/(dx)-x (d) (y(dy)/(dx)-x)^2

If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

Show that A x^2+B y^2=1 is a solution of the differential equation x{y\ (d^2y)/(dx^2)+((dy)/(dx))^2}=y(dy)/(dx)dot

Show that A x^2+B y^2=1 is a solution of the differential equation x{y\ (d^2y)/(dx^2)+((dy)/(dx))^2}=y(dy)/(dx)dot

Solve the following differential equations: (dy)/(dx)=1+x+y+x y (ii) y-x(dy)/(dx)=a(y^2+(dy)/(dx))

Solve the following differential equations: (dy)/(dx)=1+x+y+x y (ii) y-x(dy)/(dx)=a(y^2+(dy)/(dx))

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

General solution of differential equation x^(2)(x+y(dy)/(dx))+(x(dy)/(dx)-y)sqrt(x^(2)+y^(2))=0 is

The solution of y^2=2y(dy)/(dx)-((dy)/(dx))^(2), is

If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0