Change the independent variable to o in the equation `(d^2y)/(dx^2)+(2x)/(1+x^2)(dy)/(dx)+y/((1+x^2)^2)=0,` by means of the transformation `x = tan theta `

Change the independent variable to o in the equation (d^(2)y)/(dx^(2))+(2x)/(1+x^(2))(dy)/(dx)+(y)/((1+x^(2))^(2))=0, by means of the transformation x=tan theta

If y=tan^(-1)sqrt(x^(2)-1) , then the ratio (d^(2)y)/(dx^(2)):(dy)/(dx)=

If y=tan^(-1)sqrt(x^(2)-1) , then the ratio (d^(2)y)/(dx^(2)):(dy)/(dx)=

If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

If x=tan(1/alogy) , show that (1+x^2)(d^2y)/(dx^2)+(2x-a)(dy)/(dx)=0 .

If the independent variable x is changed to y, then the differential equation x(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)-(dy)/(dx)=0 is changed to x(d^(2)x)/(dy^(2))+((dx)/(dy))^(2)=k where k equals

If x=tan(1/a log y) , prove that (1+x^2) (d^2y)/(dx^2)+(2x-a) (dy)/(dx)=0

If y = tan^(-1)x show that (1+x^2)(d^2y)/(dx^2) + 2x(dy)/(dx) = 0

If x=tan(1/alogy)\ , show that (1+x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=0