Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ is the reaction rate constant. If $$x=a$$ at $$t=0$$ then solution of the equation is

$$\,{1 \over x} = {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle a$}} + k\,t$$

$$x = a\left( {1 - {e^{ - kt}}} \right)$$

GATE 2004 Civil Engineering PYQ — Engineering Mathematics

GATE 20042004PYQMCQanswer keyexplanation sooneasy

Engineering Mathematics · Differential Equations (CE)

Concept intelligence

Jump into a concept drill from this question.

Studying seriously for GATE CSE?

Keep browsing free. Pro unlocks the paid study loop: explanations, topic mastery, mistake notebook, and custom PYQ drills.

Recurring concept

Differential Equations (CE) has appeared in GATE Civil Engineering 63 times across 26 years (2017, 2022, 2023, 2024, 2025, ...).

More questions on Differential Equations (CE)

∑ has math

ordinary differential equationvariable separableinitial value problemfirst order ODE