The differential equation of the family of circles passing through the fixed points (a, 0) and ($$-$$a, 0) is

The differential equation of the family of curves $$y = {e^{2x}}(a\cos x + b\sin x)$$, where a and b are arbitrary constants, is given by

The slope at any point of a curve y = f(x) is given by $${{dy} \over {dx}} = 3{x^2}$$ and it passes through ($$-$$1, 1). The equation of the curve is

The general solution of the differential equation $${{dy} \over {dx}} = {e^{y + x}} + {e^{y - x}}$$ is

where c is an arbitrary constant