Differential Equation Help: Solve with Confidence

College
Calculus and Analysis
Differential Equations

Recent questions in Differential Equations

Carley Haley 2022-05-10

Find the linear approximation $Y$ to $f (x)$ near $x = a$ .
$f (x) = x + x^{4}, a = 0$

syaoronsangelhwc17 2022-05-09

Use linear approximation to approximate $1 / 0.254$ .

Angelique Horne 2022-05-09

Use linear approximation, i.e. the tangent line, to approximate ${11.2}^{2}$ as follows :
Let $f (x) = x^{2}$ and find the equation of the tangent line to $f (x)$ at $x = 11$ . Using this, find your approximation for ${11.2}^{2}$ .

Alexis Meyer 2022-05-09

Use the linear approximation of $f (x, y, z) =$ at $(- 2, 1, 1)$ to estimate $f (- 1.98, 0.97, 1.03)$

Paul Duran 2022-05-08

Using $f (x, y, z) = \sqrt{x + 2 y + 3 z}$ and an appropriately chosen linear approximation to find the value of $\sqrt{226}$

studovnaem4z6 2022-05-08

Let $l (x)$ be the linear approximation of $f (x) = x^{2 / 5}$ at $a = 32$ . Approximation?

ga2t1a2dan1oj 2022-05-08

Given the relations:
$\begin{aligned} F_{1} (x, y, u, v) = u e^{y} + (y + 1) e^{v x} + x y + 1 = 0 \\ F_{2} (x, y, u, v) = x + y + x u + e^{y + v} - 1 = 0 \end{aligned}$
find the linear approximation of $(u, v)$ in terms of $(x, y)$ near $(x, y, u, v) = (0, 0, - 2, 0)$ .

ashish.singh2021 2022-05-04

veleumnihryz 2022-05-03

Use suitable linear approximation to find the approximate values for given functions at the points indicated:
$f (x, y) = x e^{y + x^{2}}$

y''+4y= f(t); y(0)= 1, y''(0)=0 , with
f(t) = { 0 for 0≤t<4 , 3 for t≥4}

Jazmine Sweeney 2022-04-30

$\int_{0}^{\infty} {\cos (x t) o v e r 1 + t^{2}} d t$
I'm supposed to solve this using Laplace Transformations.

y"+4y= $\int_{1}^{0} 0 \leq t \leq t \leq \infty$
y(0)=1
y'(0)=0

Magdalena Norton 2022-04-21

Inverse Laplace Transform without using equations
I'm stuck with a question about Inverse Laplace Transform here, but the use of inverse laplace transform equation is forbidden.
$Y (s) = \frac{e^{- π s}}{s [{(s + 1)}^{2} + 1]}$

purbahassan 2022-04-16

A large tank is partially filled with 100 gallons of fluid in which 10 pounds of
salt is dissolved. Brine containing ½ pound of salt per gallon is pumped into
the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out
at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank
after 30 minutes.

Quinn Moses 2022-04-16

Laplace transform of $f (t^{2})$
Suppose we know the Laplace transform of a function f(t):
$F (s) = \int_{0}^{\infty} f (t) e^{- s t} d t$

Erika Bernard 2022-04-15

Laplace transform of a exponential.
we know that Laplace transform of $x^{n}$ is
$L [x^{n}]$
provided n is a positive integer
but what is Laplace transform of
$a^{x}$ where a is some constant number
please help i searched on google so many times and try to solve this by its original defination that is
$L [x^{n}] = \int_{0}^{\infty} a^{x} e^{- s x} d x$
but how to solve further ( i am using x insted of t here)

Beckham Short 2022-04-15

find the laplace transform of this equation:
$4 - 4 t + 2 t^{2}$
What I am doing:
$\frac{4}{s} - \frac{4}{s^{2}} + \frac{4}{s^{3}}$
$\frac{4 s^{2} - 4 s}{s^{3}} + \frac{4}{s^{3}}$
$\frac{4 s^{2} - 4 s + 4}{s 3}$
But I am getting the wrong answer, can you please tell me what I am doing wrong?

Jakobe Norton 2022-04-15

Find the Laplace transform of $f (t) = 10 t e^{- 5 t}$

Zane Decker 2022-04-14

Laplace transform of $f (t) = t e^{- t} \sin (2 t)$

Leia Sullivan 2022-04-13

Let
$x^{} (s) = (\frac{1}{(s + μ_{1} + μ_{2}) (s + {\hat{λ}}_{2}) (s + λ_{1} + λ_{2})})$
be the laplace transform in question, where $μ_{1}, μ_{2}, λ_{1}, λ_{2}, {\hat{λ}}_{2}$ are just real parameters.
How can i get its inverse by means of convolution, $x (t) = L^{- 1} (x^{} (s))$

Speaking of differential equations, these are used not only by those students majoring in Physics because solving differential equations is also quite common in Statistics and Financial Studies. Explore the list of questions and examples of equations to get a basic idea of how it is done.

These answers below are meant to provide you with the starting points as you work with your differential equations. If you need specific help or cannot understand the rules behind the answers that are presented below, start with a simple equation and learn with the provided solutions..

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