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

If y=(x sin^(-1)x)/(sqrt(1-x^(2))), prove that (1-x^(2))(dy)/(dx)=x+(y)/(x)

If y=(x sin^(-1)x)/(sqrt(1-x^(2))), prove that (1-x^(2))(dy)/(dx)=x+(y)/(x)

If y=sqrt((1-x)/(1+x)), find (dy)/(dx) and prove that (1-x^(2))(dy)/(dx)+y=0

Solver the following differential equation : (1) x(dy)/(dx) + 2y =x^(2) .log x

For each of the following differential equations verify that the accompanying functions a solution.Differential Function x(dy)/(dx)=yy=axx+y(dy)/(dx)=0y=+-sqrt(a^(2)-x^(2))x(dy)/(dx)y=y^(2)y=(a)/(x+a)x^(3)(d^(2)y)/(dx^(2))=1y=ax+b+(1)/(2x)y=((dy)/(dx))^(2)y=(1)/(4)(x+-a)^(2)

If y=xsin^(-1)x+sqrt(1-x^2) then (dy)/(dx)=

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

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