Differential Equations Questions with Solutions

14 questions1 easy10 medium3 hard

A differential equation is an equation involving a function and its derivatives. This topic covers the order and degree of a differential equation, forming a differential equation by eliminating arbitrary constants, and solving first-order equations. The main solution methods are variables separable, homogeneous equations (using the substitution y = vx), and linear equations of the form dy/dx + Py = Q, solved with the integrating factor e^(integral of P dx). Exam questions also include application problems on growth and decay, such as population growth, radioactive decay and Newton's law of cooling. Remember that the degree is defined only when the equation is a polynomial in its derivatives. Practise the differential equations questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
A company models the rate of change of concentration by $(y^{2} + 3 x y) d x + (x^{2} + x y) d y = 0$ , with $y = 1$ when $x = 1$ . Find $y$ as a function of $x$ .
A. $\frac{x ^{2}}{x + 1}$ B. $\frac{x + 1}{x ^{2}}$ C. $x + 1$ D. $x (- 1 + 1 + \frac{3}{x ^{4}})$
hardAsked in MAH MCA CET 2025View solution ›
Q2.
A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant $= k > 0$ ). Find the time after which the cone is empty.
A. $T = \frac{H}{k}$ B. $T = H k$ C. T=H%kD. T=0
hardAsked in MAH MCA CET 2024View solution ›
Q3.
Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of
A. circlesB. parabolasC. hyperbolasD. straight lines
hardAsked in NIMCET 2018View solution ›