Explore Laplace Transform Equations

Solve the differential equation:
$y^{'} (x) = y (x) - x - 1 + \frac{1}{x - y (x) + 2}$
with initial condition $y (0) = 0$

$(y - x y^{2}) d x + (x + x^{2} y^{2}) d y = 0; when y (1) = 1$

abreviatsjw 2022-01-03

The population of a certain country is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000. Estimate the initial population of the nation and find an expression for the country's approximate population at any time.

oliviayychengwh 2022-01-03

Brine containing 1.5lb/gal of salt enters a tank at the rate of 2gal/min and the mixture well stirred leaves at the same rate. The tank initially contains 100 gal of brine with10 lbs of dissolved salt. When will the amount of salt in the tank be 20 lbs?

quiquenobi2v6 2022-01-03

Identify the following linear differential equation.
$x^{2} y^{'} + y^{2} = 0$

Chris Cruz 2022-01-02

Non-Homogeneous Linear Differential Equation (The Method of Undetermined Coefficients).
Solve the equation $(D + 1) y = \sin x$

ajedrezlaproa6j 2022-01-02

Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium decompose to 96mg. How many mg will be left after another 100 years What is the "half life" (the time required to decompose half the initial amount) of radium?

Gregory Emery 2022-01-01

$y^{'} + \frac{1}{x} y = \cos (x)$

guringpw 2021-12-31

Solve the following manually using separable differential equations method.
$m y d x + n x d y = 0$

David Lewis 2021-12-31

$x y d x + {\frac{1}{2} x^{2} (1 - y \ln y - y)} d y = 0$

veksetz 2021-12-31

Identify the characteristic equation, solve for the characteristic roots, and solve the 2nd order differential equations.
$(18 D^{3} - 33 D^{2} + 20 D - 4) y = 0$

percibaa8 2021-12-31

A 8 volt battery is connected to a series circuit in which the inductance is 4 henry and the resistance is 5 ohms. Find the current if the initial current is zero. What will the current be after a very long time?

Helen Lewis 2021-12-31

$y (x^{2} + x y - 2 y^{2}) d x + x (3 y^{2} - x y - x^{2}) d y = 0; w h e n x = 1, y = 1$

Painevg 2021-12-31

Solve for G.S. / P.S. for the following differential equations using the method of solution for homogeneous equations.
$- (3 x + 25 y) d x + (25 x + 3 y) d y = 0$

nemired9 2021-12-31

When a body is removed from an oven, its temperature is measured at $230^{\circ} F$ . Four minutes later its temperature is $120^{\circ} F$ . If the room temperature is found to be $70^{\circ} F$ , how long will it take for the chicken to cool off to a temperature of $90^{\circ} F$ . What is the steady state temperature of the body?

Kelly Nelson 2021-12-31

Solve for the general solution of the differential equation $(x + 2 y - 1) d x + (2 x + 4 y - 3) d y = 0$ using Substitution Suggested by the Equation.

jamessinatraaa 2021-12-31

$\frac{d y}{d x} = - \frac{a x + b y}{b x + c y}$

Gregory Emery 2021-12-31

Find the differential equations of the following. Show complete solution. $\frac{d y}{d x} + y = e^{2 x}$

If you came across the necessity of Laplace transform, it is most likely that you are coming from a mechanical engineering or electrical background. The concept is used to solve differential equations, which is why it is vital to consider Laplace transform examples as you are looking through the questions and connect the dots as the equations are being approached. Remember to look through our list of answers as these will help you to address various Laplace transform problems and find solutions to complex Laplace transform questions as you are dealing with your Laplace transform equation homework.

Differential Equations