Sketching solutions. Each of the differential equations in
Exercise Group 1.3.8.14-19 has several initial conditions specified. Sketch the
solution curves that satisfy the initial conditions. Sketch your solutions for each
equation on the same pair of axes.
14. $y' = 2y - 5$, $y(0) = 4$, $y(0) = 2$, $y(0) = 0$.
$\frac{dx}{dt} = (x - 1)(x + 2)$, $x(0) = 2$, $x(0) = 1$, $x(0) = 0$.
$\frac{dx}{dt} = (x^2 - 1)(x - 2)$, $x(0) = 1$, $x(0) = 0$, $x(0) = -1$.
$\frac{dy}{dx} = \sin 2y$, $y(0) = 2$, $y(0) = 1$, $y(0) = 0$.
18. $x' = (x^2 + 1)(x - 1)$, $x(0) = 2$, $x(0) = 1$, $x(0) = 0$.
19. $x' = x^2 + x + 1$, $x(0) = 1$, $x(0) = 0$, $x(0) = -1$.
