Question

The figure shows the plot of y as a function of x. The function shown is the solution of the differential equation (assuming all initial condition to be zero) is

• A. $\frac{d^{2}y}{d{x}^2}=1$
• B. $\frac{dy}{dx}=-x$
• C. $\frac{dy}{dx}=-x$
• D. $\frac{dy}{dx}=\left|x\right|$

Answer 1

The correct option is D $\frac{dy}{dx}=\left|x\right|$

From the graph

y = $\{\begin{array}{cc}\frac{x^2}{2};& x\ge 0\\ -\frac{x^2}{2};& x\le 0\end{array}$

$\Rightarrow \frac{dy}{dx}=\{\begin{array}{cc}x;& x\ge 0\\ -x;& x\le 0\end{array}=\left|x\right|$

(By definition of Mod)