Differential Equations and Linear Algebra - Math Questions and Answers

Recent questions in Differential equations

Eliza Shields 2023-03-24

The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_{1} e^{x} + c_{2} e^{2 x}$
B) $c_{1} e^{- x} + c_{2} e^{3 x}$
C) $c_{1} e^{- x} + c_{2} e^{- 2 x}$
D) $c_{1} e^{- 2 x} + c_{2} 2^{- x}$

Zachariah Ferrell 2023-03-24

How to differentiate $y = \log x^{2}$ ?

Kara Cummings 2023-03-21

The differential coefficient of $\sec (\tan^{- 1} (x))$ .

Jadiel Bowers 2023-02-25

Let $f$ be a twice differentiable function such that $g' (x) = - f (x)$ and $f' (x) = g (x)$ , $h (x) = {(f (x))}^{2} + {(g (x))}^{2}$ . If $h (5) = 11$ , then $h (10)$ is equal to
A. $22$
B. $11$
C. $0$
D. $20$

sosterrm0m 2023-02-25

What is the differentiation of $u v$ ?

rehaucesnwr1 2023-02-23

Let f be a differentiable function such that $f^{'} (x) = 7 - \frac{3}{4} * \frac{f (x)}{x}, (x > 0)$ and $f (1) \neq 4$ . Then $lim_{x \to 0^{+}} x * f (\frac{1}{x}) :$
A)does not exist.
B)exists and equals 4.
C)exists and equals 4/7.
D)exists and equals 0.

Kamenemoj3q 2023-02-18

What are the absolute extrema of $f (x) = x^{3} - 3 x + 1 \in [0, 3]$ ?

Damaris Bradshaw 2023-02-13

$x y^{2} \cdot (\frac{d y}{d x}) = y^{3} - x^{3}, y (1) = 2$ (its a initial value problem) Any kind soul here who can give the solution of this eqn?

ulovljenolq3 2023-02-07

The graph of the linear equation 2x + 3y = 6 meets the y - axis at the point:
(a) (2, 0);
(b) (3, 0);
(c) (0, 2);
(d) (0, 3)

Deacon Hensley 2023-01-20

Differentiate $x e^{x}$ using first principle.

Talan Mercer 2023-01-08

Write the first four terms of the A.P. when the first term a and the common difference d are given as follows: (iii) a=4, d=-3.

Lizeth Herring 2022-12-27

Let f be a differentiable function on R satisfying $f' (t) = e^{t} (\cos^{2} t - s i n 2 t)$ and f(0)=1, then which of the following is/are correct ?
A) f is bounded in $t \in (- \infty, 0)$
B) number of solutions satisfying the equation $f (t) = e^{t}$ in [0,2π] is 3
C) $lim_{t \to 0} f (t))^{1 / t} = 1$
D) f is an even function

sublimnoj7u7 2022-12-26

Derivative of $f (x) = 4 e^{x} - 4^{x} + 2 \ln x$ is
A) $4 e^{x} - 4^{x} \ln 4 + \frac{2}{x}$
B) $4 e^{x} + 4^{x} \ln 4 + \frac{2}{x}$
C) $4 e^{x} - 4^{x} \ln 4 - \frac{2}{x}$
D) $4 e^{x} - 4^{x} \ln 4 + 2 x$

Alaina Durham 2022-12-21

If $y = x^{sinx},$ then $\frac{dy}{dx} = ?$
A) $\frac{x^{\sin x} (x \cos x \log x + \sin x)}{x}$
B $\frac{x^{sinx} (xcosxlogx + \cos x)}{x}$
C) $\frac{y (xcosxlogx + cosx)}{x}$
D) None of these

Kason Wong 2022-12-21

What is the Solution of the Differential Equation $\frac{d P}{d t} = k P - A P^{2}$ ?

Emilia Carpenter 2022-12-05

Name two warning signs of suspect health products/services being offered on the Internet

alistianyStu 2022-12-02

Prove that the equation $4^{x} = 8 x + 1$ has only one solution

Julius Ho 2022-12-02

Consider the differential equation $\frac{d y}{d t} = a y - b$ .
Find the equilibrium solution $y_{e}$

e3r2a1cakCh7 2022-12-01

Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is?

Brenda Leach 2022-11-29

Solve the given initial-value problem. The DE is homogeneous.
$x y^{2} \frac{d y}{d x} = \frac{y^{3}}{x^{3}}$

One of the most challenging parts of Calculus 2 relates to differential equations. It’s recommended to start with the ordinary differential equations as these will help you understand the concepts. If you are not sure how to work with variables and functions, start with at least one equation that is provided in differential equations examples. See the unknown function and seek the answers by comparing what you have available. The majority of differential equations problems will provide you with the basics. If you are not sure how to find differential equations solutions, think about the relationship between functions and derivatives.

Calculus 2

Differential Equations and Linear Algebra Q&A