Home › MHT-CET › Mathematics › Differential Equations › The differential equation of the family of strai…
The differential equation of the family of straight lines $y = mx + c$ (with $m, c$ arbitrary) is:
A$d^2y/dx^2 = 0$
B$dy/dx = 0$
C$d^2y/dx^2 = m$
D$y = x\,dy/dx$
Answer & Solution
Correct answer: A. $d^2y/dx^2 = 0$
Two arbitrary constants $m, c$ ⇒ second-order DE. Differentiate twice: $dy/dx = m$, then $d^2y/dx^2 = 0$. Every straight line has zero curvature.
Related questions
Reducing $(2x-1)\dfrac{d^2y}{dx^2}-2\dfrac{dy}{dx}=0$ with $y=2$ and $\dfrac{dy}{dx}=3$ atA village grows at a rate proportional to its population. It was 20,000 in 1999 and 25,000For $\dfrac{d^2y}{dx^2}+3\dfrac{dy}{dx}+2y=6e^{x}+ in x$, the particular integral is:The complementary function of $\dfrac{d^2y}{dx^2}+3\dfrac{dy}{dx}+2y=6e^{x}+ in x$ is:Solutions of a differential equation form a set that is a:The power counted for the degree must be a whole number that is:An equation whose highest derivative is the third has order:The study at this stage is confined to equations that are: