A differential equation of the form `dy/dx+Py=Q` is said to be a linear differential equation. Integrating factor of this differential equation is `e^(intPdx)` and its solution is given by `y.e^(int Pdx)=int (Qe^(int Pdx))dx+c`. Answer the question:Solution of differential equation `(1+y^2)dx+(x-e^(-tan^-1y)dy=0` is (A) `y=tan^-1x+c` (B) `ye^(tan^-1x)=tan^-1x+c` (C) `xe^(tan^-1y)=tan^-1y+c` (D) none of these

The solution of differential equation (1+y^(2))+(x-e^(tan^(-1)y))(dy)/(dx)=0 , is

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

A differential equation of the form dy/dx+Py=Q is said to be a linear differential equation. Integrating factor of this differential equation is e^int Pdx and its solution is given by y.e^(int Pdx)=int (Qe^(int Pdx))dx+c . Answer the question:Let f(x) be a differentiable function in intervel (0, oo) such that f(1)=1 and lim_(trarrx) (t^2f(x)-x^2f(t))/(t-x)=1 for all x gt 0 . Then f(x) = (A) 1/(3x)+(2x^2)/3 (B) -1/(3x)+(4x^2)/3 (C) -1/x+2/x^2 (D) 1/x

The solution of differential equation (1+x^(2)) (dy)/(dx) + y = e^(tan^(-1)x)

The general solution of the differential equation y dx +(1+x^2) tan^(-1) x dy =0 is