Mathematics · Physics

Differential Equations

247 Questions

Differential equations involve finding functions that relate variables to their rates of change. These questions cover first and second order equations and separation of variables. They are a core part of the mathematics syllabus for high level competitive exams.

First order separationSecond order linear equationsInitial value problemsPredator prey modelsCauchy Riemann equations

Differential Equations Questions

Multiple choice general knowledge math & puzzles

solve the differential equation: dy/dx = y/x

xK where x does not exist
Kx where K = +-e to the power of C
Kx where K does not exist
xK where x = +-e to the power of C

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Multiple choice general knowledge

Which solver would be preferred for a model containing continuous signals and continuous states?

Fixed-step discrete solver
Fixed-step ODE type solver
Variable-step discrete solver
Variable-step ODE type solver

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Multiple choice

The following differential equation has $3\frac{d^2y}{dt^2}+4\bigg(\frac{dy}{dt}\bigg)^3+y^2 + 2 = x$

degree = 2, order = 2
degree = 1, order = 2
degree = 4, order = 3
degree = 2, order = 3

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Multiple choice

A solution of the following differential equation is given by $\frac{d^2y}{dx^2}-5\frac{dy}{dx}+6y = 0$

$y = e^{2x} + e^{-3x}$
$y = e^{2x} + e^{3x}$
$y = e^{-2x} + e^{3x}$
$y = e^{-2x} + e^{-3x}$

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Multiple choice

A solution for the differential equation $x(t) + 2x(t) = \delta(t)$with initial condition x (0 ^-) = 0 is

e^-2t u (t)
e^2t u (t)
e^-t u (t)
e^t u (t)

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Multiple choice

For the differential equation $\frac{d^2y}{dx^2}$+ k²y = 0 the boundary conditions are (i) y = 0 for x = 0 and (ii) y = 0 for x = a The form of non-zero solutions of y (where m varies over all integers) are

y = $\sum_m A_m sin \frac{m \pi x}{a}$
y = $\sum_m A_m cos \frac{m \pi x}{a}$
y = $\sum_m A_m \times \frac{m \pi }{a}$
y = $\sum_m A_m e \frac{m \pi x}{a}$

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Multiple choice

The solution of the differential equation K² ^{$\frac{d^2y}{dx^2}$}= y – y₂ under the boundary conditions (i) y = y₁ at x = 0 and (ii) y = y₂ at x = ^_$\infty$, where k, y₁ and y₂ are constants, is

y = (y₁– y₂) exp (– x/k²) + y₂
y = (y₂– y₁) exp (– x/k) + y₁
y = (y₁– y₂) sinh (– x/k) + y₁
y = (y₁– y₂) exp (– x/k) + y₂

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Multiple choice

Which of the following is a solution to the differential equation$\frac{dx(t)}{dt} + 3x (t)$= 0?

x (t) = 3e^t
x (t) = 2e^-3t
x (t) = -$\frac{3}{2} t^2$
x (t) = 3t²

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Multiple choice

The order of the differential equation ^{$\frac{d^2y}{dt^2}+\Big(\frac{dy}{dt}\Big)^3$}+ y⁴ = e^-tis

1
2
3
4

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Multiple choice

Match each differential equation in Group I to its family of solution curves in Group II:

A - 2, B - 3, C - 3, D - 1
A - 1, B - 3, C - 2, D - 1
A - 2, B - 1, C - 3, D - 3
A - 3, B - 2, C - 1, D - 2

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Multiple choice

The solution of the differential equation ^{$\frac{dy}{dx}$}= ky, y (0) = c is

x = ce^−ky
x = ke^cy 
y = ce^kx
y = ce^−kx

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Multiple choice

The solution of the differential equation ^{$\frac{d^2 y}{dt^2} + 2 \frac{dy}{dt} + y = 0$}with y(0) = y’ (0) = 1 is

(2 - t) e^t
(1 + 2t)e ^-^t
(2 + t)e ^-^t
(1 - 2t)e^t

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Multiple choice

If the characteristic equation of the differential equation ^{$\frac{d^2 y}{dx^2} + 2 \alpha \frac{dy}{dx} + y = 0$}has two equal roots, then the values of a are

^$\pm$1
0, 0
^$\pm$j
^$\pm$1/2

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Multiple choice

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. ^{$\begin{matrix}
\ . \
\ y \
\end{matrix}$} (t) + 5y(t) = u(t) when y(0) = 1 and u(t) is a unit step function, y(t) is

0.2 + 0.8e-^5t
0.2 - 0.2e-^5t
0.8 + 0.2e-^5t
0.8 - 0.8e-^5t

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Multiple choice

A function n(x) satisfied the differential equation $\frac{d^2 n(x)}{dx^2} - \frac{n(x)}{L^2}$ = 0 where L is a constant. The boundary conditions are: n(0) = K and n (∞) = 0. The solution to this equation is

n(x) = K exp(x/L)
n(x) = K exp(-x/$\sqrt{5}$)
n(x) = K² exp(-x/L)
n(x) = K exp(-x/L)

Reveal answer Fill a bubble to check yourself

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