Differential Equations

Question 1

Multiple choice general knowledge math & puzzles

Solve y = x^3+(sqrt5) Note: Differentiate with respect to "x" (sqrt is Square root)

dy/dx = 3x^2+5
dy/dx = 3x+2.5
dx/dy = 2x^3+(sqrt2.5)

Reveal answer Fill a bubble to check yourself

Answer

dy/dx = 3x^2

Question 2

Multiple choice general knowledge math & puzzles

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

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

Reveal answer Fill a bubble to check yourself

Answer

Kx where K = +-e to the power of C

Question 3

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

Reveal answer Fill a bubble to check yourself

Answer

degree = 1, order = 2

Question 4

Multiple choice

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

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

Reveal answer Fill a bubble to check yourself

Answer

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

Question 5

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

Reveal answer Fill a bubble to check yourself

Answer

e^-2t u (t)

Question 6

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

Reveal answer Fill a bubble to check yourself

Answer

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

Question 7

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

Reveal answer Fill a bubble to check yourself

Answer

y = (y₁– y₂) exp (– x/k) + y₂

Question 8

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) = -$\frac{3}{2} t^2$
x (t) = 3t²

Reveal answer Fill a bubble to check yourself

Answer

x (t) = 2e^-3t

Question 9

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

Reveal answer Fill a bubble to check yourself

Answer

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

Answer

(1 + 2t)e ^-^t

Answer

0.2 + 0.8e-^5t

Answer

n(x) = K exp(-x/L)

Question 10

Multiple choice

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

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

Reveal answer Fill a bubble to check yourself

Question 11

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

Reveal answer Fill a bubble to check yourself

Question 12

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

Reveal answer Fill a bubble to check yourself

Question 13

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

Reveal answer Fill a bubble to check yourself

Question 14

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

Reveal answer Fill a bubble to check yourself

Question 15

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)

Reveal answer Fill a bubble to check yourself

Differential Equations

Differential Equations Questions