Step-by-step explanation:
By pressing the button that looks like this 
 
        
                    
             
        
        
        
Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2
        
             
        
        
        
The inverse of 2/3 
is 3/2. 
Good Luck! :)