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.

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Q1.
Given $\frac{d y}{d x} + y = 1$ with $y (0) = 2$ , find $y (1)$ .
A. $2 e^{- 1} + 1$ B. $e^{- 1} + 2$ C. $1 + e^{- 1}$ D. $1 - e^{- 1}$
easyAsked in MAH MCA CET 2025View solution ›