We have, $a=\frac{d^{2} x}{d t^{2}}=-9.8$ The initial conditions are $x(0)=19.6$ and $v(0)=0$ So, $v=\frac{d x}{d t}=-9.8 t+v(0)=-9.8 t$ $\therefore x=-4.9 t^{2}+x(0)=-4.9 t^{2}+19.6$ Now, the domain of the function is restricted since the ball hits the ground after a certain time. To find this time we set $x=0$ and solve for $t$. $0=4.9 t^{2}+19.6 \Rightarrow t=2$
A differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on.
Orders of a Differential Equation
First Order Differential Equation
The first-order differential equation has a degree equal to 1. All the linear equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x and y are the two variables and is represented as: dy/dx = f(x, y) = y’
Second-Order Differential Equation
The equation which includes second-order derivative is the second-order differential equation. It is represented as; d/dx(dy/dx) = d2y/dx2 = f”(x) = y”.
Types of Differential Equations
Differential equations can be divided into several types namely
