Let y=f(x) be the solution of differential equation `e^(-x)dy-x^(2)dx=2xdx` satisfying y(0)=0 ,then local maximum value of f(x) is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

Solution of the differential equation y dx+(x-y^(2))dy=0 is

Let y=f(x) is a solution of differential equation e^(y)((dy)/(dx)-1)=e^(x) and f(0)=0 then f(1) is equal to

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

If y = y (x) is the solution of the differential equation (5 + e^(x))/(2 + y) * (dy)/(dx) + e^(x) = 0 satisfying y(0) = 1 , then a value of y (log _(e) 13) is :

The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e^(x) secy satisfying y(1)=0 , is

Solution of differential equation (x-y^(2)x)dx-(y+x^(2)y)dy=0,ifx=2,y=0, is