Explore Laplace Transform Equations

Solve the differential equation $y^{'} = | x |, y (- 1) = 2$

expeditiupc 2022-01-21

Closed form solutions of $\ddot{x} (t) - x {(t)}^{n} = 0$

Derive the Laplace transform of the following unction: cos bt

Michael Maggard 2022-01-20

Find y which satisfies:
$y^{'} = y^{a}, y (a) = a - 2$ , for $a \in N$

killjoy1990xb9 2022-01-20

Solving simple differential equation
$(t + 4) d x = 4 (1 + x^{2}) d t$

veksetz 2022-01-20

How to solve $\frac{d y}{d x} = 5 x y + \sin x$ ?
With $y (0) = 1$ . Use an integrating factor.

Pam Stokes 2022-01-20

How to find $x \frac{d y}{d x} = y + \frac{4}{x}$ ?
It's given that $x > 1, y = 1 when x = 1$ .

burkinaval1b 2022-01-20

Question about solving a differential equation
$D (D - 3) (D + 4) [y] = 0$ ,
where D is the differential operator, how to get the general solution of y? The solution suggest that it is
$y = 6 c_{1} - 2 c_{2} \exp (- 4 t) + 3_{c_{3}} \exp (3 t)$

berljivx8 2022-01-20

$y_{1}, y_{2}, y_{3}$ are particular solutions of $y^{'} + a (x) y = b (x)$ , so the function $\frac{y_{2} - y_{3}}{y_{3} - y_{1}}$ is constant.

Helen Lewis 2022-01-20

What might be a solution to the differential equation of the form
$x y = c \frac{y}{y + d}$
where $y = y (x)$ and c,d are constants? I am supposed to simply state a solution to this, but I don;t think it is all that obvious.

Mary Jackson 2022-01-20

I was reading some of my notes and I was not sure how the following works:
$\frac{d^{2} y}{{d x}^{2}} + \frac{d y}{d x} = 0$
Solve the above with the condition $y (0) = 0$
$\Rightarrow y (x) = A (1 - e^{- x})$ with A an arbitrary constant.
I was just wondering how do you solve the above to get
$y (x) = A (1 - e^{- x})$ ? Because when I tried it, I got:
$y = A + B e^{- x}$ , and using the condition $y (0) = 0$ , I got $A + B = 0$ .

stop2dance3l 2022-01-20

The author of my textbook asks to verify that the function:
$y = \sqrt{\frac{2}{3} \ln (1 + x^{2}) + C}$
solves the differential equation
$\frac{d y}{d x} = \frac{x^{3}}{y + y x^{3}}$
However, this is an error and this y does not solve the differential equation. Is there a simple typo that makes the problem workable?

tripiverded9 2022-01-20

$y^{‴} - y = x^{2}$ has solution ''multiplicity''?

Anne Wacker 2022-01-20

Solve fractional differential equation?
$\frac{d^{2}}{{d x}^{2}} u (x) + b \frac{d^{\frac{1}{k}}}{{d x}^{\frac{1}{k}}} u (x) + c u (x) = 0$
assuming $(a, b, c) = c o n s t$ and k a parameter?

sunshine022uv 2022-01-20

Solution for a non linear ODE
$u^{'} = u^{2}$

Tara Alvarado 2022-01-20

solving second order linear ODE
$\frac{a}{x} y^{'} (x) + \frac{1}{2} y^{″} (x) = 0$
where a is a constant. Also how can I solve this equation if the right hand side is different than zero?

Agohofidov6 2022-01-20

Suppose that Canada has a total of $10 billion in $20 bills in circulation, and each day $40 million of these $20 bills passes through one bank or another. A new harder-to-forge version of the $20 bill is developed, and the banks replace the old bills with new ones whenever they can. How long does it take for the new bills to reach 90% of the total number of $20 bills in circulation?

veksetz 2022-01-20

Some double angle identity to solve $(2 x^{2} + y^{2}) \frac{d y}{d x} = 2 x y ?$

hadejada7x 2022-01-20

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

Maria Huey 2022-01-20

I need to calculate a taylor polynomial for a function $f : R \to R$ where we know the following
$f^{″} (x) + f (x) = e^{- x} \forall x$
$f (0) = 0$
$f^{'} (0) = 2$

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

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