Solve: \(\frac { dy }{ dx } \) = sin(x + y)

Solve: x²\(\frac { dy }{ dx } \) = y²+2xy given that y = 1, when x = 1

Solve: (y-x)\(\frac { dy }{ dx } \) = a²

Solve: (D² + 14D + 49)y = e^-7x + 4.

The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation \(\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } } \). Find the relationship between c and q if c = 1 when q = 1.