Recent questions in Differential equations

Calculus 2Answered question

Eliza Shields 2023-03-24

The solution of a differential equation y′′+3y′+2y=0 is of the form

A) ${c}_{1}{e}^{x}+{c}_{2}{e}^{2x}$

B) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{3x}$

C) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{-2x}$

D) ${c}_{1}{e}^{-2x}+{c}_{2}{2}^{-x}$

A) ${c}_{1}{e}^{x}+{c}_{2}{e}^{2x}$

B) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{3x}$

C) ${c}_{1}{e}^{-x}+{c}_{2}{e}^{-2x}$

D) ${c}_{1}{e}^{-2x}+{c}_{2}{2}^{-x}$

Calculus 2Answered question

Zachariah Ferrell 2023-03-24

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

Calculus 2Answered question

Kara Cummings 2023-03-21

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

Calculus 2Answered question

Jadiel Bowers 2023-02-25

Let $f$ be a twice differentiable function such that $g\text{'}\left(x\right)=-f\left(x\right)$ and $f\text{'}\left(x\right)=g\left(x\right)$, $h\left(x\right)={\left(f\left(x\right)\right)}^{2}+{\left(g\left(x\right)\right)}^{2}$. If $h\left(5\right)=11$, then $h\left(10\right)$ is equal to

A. $22$

B. $11$

C. $0$

D. $20$

A. $22$

B. $11$

C. $0$

D. $20$

Calculus 2Answered question

rehaucesnwr1 2023-02-23

Let f be a differentiable function such that ${f}^{\prime}(x)=7-\frac{3}{4}\ast \frac{f(x)}{x},(x>0)$ and $f(1)\ne 4$. Then $\underset{x\to {0}^{+}}{lim}x\ast f(\frac{1}{x}):$

A)does not exist.

B)exists and equals 4.

C)exists and equals 4/7.

D)exists and equals 0.

A)does not exist.

B)exists and equals 4.

C)exists and equals 4/7.

D)exists and equals 0.

Calculus 2Answered question

Kamenemoj3q 2023-02-18

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

Calculus 2Answered question

Damaris Bradshaw 2023-02-13

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

Calculus 2Answered question

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)

(a) (2, 0);

(b) (3, 0);

(c) (0, 2);

(d) (0, 3)

Calculus 2Answered question

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.

Calculus 2Answered question

Lizeth Herring 2022-12-27

Let f be a differentiable function on R satisfying $f\prime (t)={e}^{t}({\mathrm{cos}}^{2}t-sin2t)$ and f(0)=1, then which of the following is/are correct ?

A) f is bounded in $t\in (-\mathrm{\infty},0)$

B) number of solutions satisfying the equation $f(t)={e}^{t}$ in [0,2π] is 3

C) $\underset{t\to 0}{lim}f(t){)}^{1/t}=1$

D) f is an even function

A) f is bounded in $t\in (-\mathrm{\infty},0)$

B) number of solutions satisfying the equation $f(t)={e}^{t}$ in [0,2π] is 3

C) $\underset{t\to 0}{lim}f(t){)}^{1/t}=1$

D) f is an even function

Calculus 2Answered question

sublimnoj7u7 2022-12-26

Derivative of $f(x)=4{e}^{x}-{4}^{x}+2\mathrm{ln}x$ is

A) $4{e}^{x}-{4}^{x}\mathrm{ln}4+\frac{2}{x}$

B) $4{e}^{x}+{4}^{x}\mathrm{ln}4+\frac{2}{x}$

C) $4{e}^{x}-{4}^{x}\mathrm{ln}4-\frac{2}{x}$

D) $4{e}^{x}-{4}^{x}\mathrm{ln}4+2x$

A) $4{e}^{x}-{4}^{x}\mathrm{ln}4+\frac{2}{x}$

B) $4{e}^{x}+{4}^{x}\mathrm{ln}4+\frac{2}{x}$

C) $4{e}^{x}-{4}^{x}\mathrm{ln}4-\frac{2}{x}$

D) $4{e}^{x}-{4}^{x}\mathrm{ln}4+2x$

Calculus 2Answered question

Alaina Durham 2022-12-21

If $y={x}^{\mathrm{sinx}},$ then $\frac{\mathrm{dy}}{\mathrm{dx}}=?$

A) $\frac{{x}^{\mathrm{sin}x}\left(x\mathrm{cos}x\mathrm{log}x+\mathrm{sin}x\right)}{x}$

B$\frac{{x}^{\mathrm{sinx}}\left(\mathrm{xcosxlogx}+\mathrm{cos}x\right)}{x}$

C) $\frac{y\left(\mathrm{xcosxlogx}+\mathrm{cosx}\right)}{x}$

D) None of these

A) $\frac{{x}^{\mathrm{sin}x}\left(x\mathrm{cos}x\mathrm{log}x+\mathrm{sin}x\right)}{x}$

B$\frac{{x}^{\mathrm{sinx}}\left(\mathrm{xcosxlogx}+\mathrm{cos}x\right)}{x}$

C) $\frac{y\left(\mathrm{xcosxlogx}+\mathrm{cosx}\right)}{x}$

D) None of these

Calculus 2Answered question

Kason Wong 2022-12-21

What is the Solution of the Differential Equation $\frac{dP}{dt}=kP-A{P}^{2}$ ?

Calculus 2Answered question

Emilia Carpenter 2022-12-05

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

Calculus 2Answered question

alistianyStu 2022-12-02

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

Calculus 2Answered question

Julius Ho 2022-12-02

Consider the differential equation $\frac{dy}{dt}=ay-b$.

Find the equilibrium solution ${y}_{e}$

Find the equilibrium solution ${y}_{e}$

Calculus 2Answered question

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?

Calculus 2Answered question

Brenda Leach 2022-11-29

Solve the given initial-value problem. The DE is homogeneous.

$x{y}^{2}\frac{dy}{dx}=\frac{{y}^{3}}{{x}^{3}}$

$x{y}^{2}\frac{dy}{dx}=\frac{{y}^{3}}{{x}^{3}}$

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.