The general solution of the differential equation

$$\sqrt {1 + {x^2} + {y^2} + {x^2}{y^2}} $$ + xy$${{dy} \over {dx}}$$ = 0 is :

(where C is a constant of integration)

Let y = y(x) be the solution of the differential equation

cosx$${{dy} \over {dx}}$$ + 2ysinx = sin2x, x $$ \in $$ $$\left( {0,{\pi \over 2}} \right)$$.

If y$$\left( {{\pi \over 3}} \right)$$ = 0, then y$$\left( {{\pi \over 4}} \right)$$ is equal to :

If y = y(x) is the solution of the differential

equation $${{5 + {e^x}} \over {2 + y}}.{{dy} \over {dx}} + {e^x} = 0$$ satisfying y(0) = 1, then a value of y(log_e13) is :

The solution of the differential equation

$${{dy} \over {dx}} - {{y + 3x} \over {{{\log }_e}\left( {y + 3x} \right)}} + 3 = 0$$ is:

(where c is a constant of integration)