Differential Equation Help: Solve with Confidence

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Calculus and Analysis
Differential Equations

Recent questions in Differential Equations

Albarellak 2021-01-31

Hi! This is a test question. Please enjoy it reponsibly.
Testing testing.
$f x == \int_{\infty}^{- \infty} f ξ (e^{2} π ξ x) d ξ$

babeeb0oL 2021-01-30

Use Laplace transform to find the solution of the IVP
$2 y^{'} + y = 0, y (0) = - 3$
a) $f (t) = 3 e^{- 2 t}$
b) $f (t) = 3 e^{\frac{t}{2}}$
c) $f (t) = 6 e^{2 t}$
d) $f (t) = 3 e^{- \frac{t}{2}}$

Armorikam 2021-01-28

Solve differential equation $y^{'} + 2 x y = 4 x$

e1s2kat26 2021-01-28

One solution of the differential equation $y " - 4 y = 0$ is $y = e^{2 x}$ . Find a second linearly independent solution using reduction of order.

chillywilly12a 2021-01-28

Operate the Laplace Transform on the following
$(i) f (t) = \cos (3 t)$
$(ii) f (t) = t^{\frac{1}{2}}$

permaneceerc 2021-01-27

If the Laplace Transforms of fimetions $y_{1} (t) = \int_{0}^{\infty} e^{- s t} t^{3} d t, y_{2} (t) = \int_{0}^{\infty} e^{- s t} \sin 2 t d t, y_{3} (t) = \int_{0}^{\infty} e^{- s t} e^{t} t^{2} d t$ exist , then Which of the following is the value of $L {y_{1} (t) + y_{2} (t) + y_{3} (t)}$
$a) \frac{3}{(s^{4})} + \frac{2}{(s^{2} + 4)} + \frac{2}{(s - 1)^{3}}$
$B) \frac{(3!)}{(s^{3})} + \frac{s}{(s^{2} + 4)} + \frac{(2!)}{(s - 1)^{3}}$
$c) \frac{3!}{(s^{4})} + \frac{2}{(s^{2} + 2)} + \frac{1}{(s - 1)^{3}}$
$d) \frac{3!}{(s^{4})} + \frac{4}{(s^{2} + 4)} + \frac{2}{(s^{3})} \cdot \frac{1}{(s - 1)}$
$e) \frac{3!}{(s^{4})} + \frac{2}{(s^{2} + 4)} + \frac{2}{(s - 1)^{3}}$

Carol Gates 2021-01-27

Derive the transform of $f (t) = \sin k t$ by using the identity $\sin k t = \frac{1}{2} u (e^{i k t} - e^{- i k t})$

Caelan 2021-01-27

Please solve the 2nd order differential equation by (PLEASE FOLLOW GIVEN METHOD) LAPLACE TRANSFORMATION
ALSO, USE PARTIAL FRACTION WHEN YOU ARRIVE
$L (y) = [\frac{w}{(s^{2} + a^{2}) (s^{2} + w^{2})}] \cdot b$
Problem 2 Solve the differential equation
$\frac{d^{2} y}{d t^{2}} + a^{2} y = b \sin (ω t)$ where $y (0) = 0$
and $y^{'} (0) = 0$

Amari Flowers 2021-01-27

Cosider the system of differential equations
$x_{1}^{'} = 2 x_{1} + x_{2}$
$x_{2}^{'} = 4 x_{1} - x_{2}$
Convert this system to a second order differential equations and solve this second order differential equations

Aneeka Hunt 2021-01-27

Prove $F (s) = \frac{1}{s - 2} then f (t)$ is
a) $e^{2 t} u (t)$
b) $u (t + 2)$
c) $u (t - 2)$
d) $e^{- 2 t} u (t)$

allhvasstH 2021-01-25

Use the Laplace transform to solve the given system of differential equations.
$\frac{(d^{2} x)}{(d t^{2})} + \frac{(d^{2} y)}{(d t^{2})} = \frac{t}{2}$
$\frac{(d^{2} x)}{(d t^{2})} - \frac{(d^{2} y)}{(d t^{2})} = 4 t$
$x (0) = 5, x^{'} (0) = 0,$
$y (0) = 0, y^{'} (0) = 0$

Rui Baldwin 2021-01-23

Laplace transform of $\sin (2 t) + e^{t} \sin (t)$

e1s2kat26 2021-01-22

Solve: $x \frac{d y}{d x} = 1 - y^{2}$

Lewis Harvey 2021-01-22

Use Laplace transform to solve the folowing initial value problem $y " + 2 y^{'} + y = 4 e^{- t} y (0) = 2 y^{'} (0) = - 1$

Lennie Carroll 2021-01-19

Use Laplace transforms to solve the following initial value problem
$x " - 25 x = 9 t$
$x (0) = x^{'} (0) = 0$

York 2021-01-19

A tank contains 70 gallons of pure water. A brine solution with 2 lbs/gal of salt enters at 2.25 gal/min and the well - stirred mixture leaves at the same rate. Find the amount of salt in the tank at any time and the time at which the brine leaving the tank will contain 15 lbs of salt.

Lewis Harvey 2021-01-19

determine $L^{- 1} (F)$
$F (s) = \frac{4}{(s + 2)^{3}}$

Albarellak 2021-01-19

Use the Laplace transform to solve the given differential equation subject to the indicated initial conditions.
$y^{″} - 7 y^{'} + 6 y = e^{t} + δ (t - 3) + δ (t - 5)$
$y (0) = 0$
$y^{'} (0) = 0$

melodykap 2021-01-17

Using Convolution, Solve the Volterra Integral Equation:
$y (x) = 1 - e^{- x} + \int_{0}^{x} y (x - t) \sin x d t$

York 2021-01-16

Find the general solution of the first-order linear differential equation $(d y / d x) + (1 / x) y = 6 x + 2$ , for x > 0

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..

Differential Equations

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