Explore Laplace Transform Equations

Solve the given differential equation by undetermined coefficients
$y^{″} - 14^{'} + 49 y = 35 x + 4$

William Collins 2021-12-19

Solve for the following problems using substitution suggested by the equation. $(3 x - 2 y + 1) d x + (3 x - 2 y + 3) d y = 0$

maduregimc 2021-12-19

State the order of the partial differential equation $u_{\times} + u_{y} = u + 4$ . Then classify whether it is elliptic, hyperbolic or parabolic.

Pam Stokes 2021-12-18

Obtain the solution on the following differential equations:
${(1 - x y)}^{- 2} d x + [y^{2} + x^{2} {(1 - x y)}^{- 2}] d y = 0$

William Burnett 2021-12-18

Solve the given differential equation by separation of variables.
$\frac{d S}{d r} = k S$

Helen Lewis 2021-12-18

Topic:
Exact Differential Equations
Instructions:
Solve the Exact Differential Equations of GIven Problem #2 only, ignore the other given problem.
Note:
Please answer all of the problems in the attached photo. I will rate you with “like/upvote” after; if you answer all of the problems. If not, I will rate you “unlike/downvote.” Kindly show the complete step-by-step solution.
1. $(x e^{x} y + e^{x} y) d x + (8 + x e^{x}) d y = 0; y (0) = - 4$
2. $(\frac{x + y}{y^{2} + 1}) d y + (\arctan y + x) d x = 0$

Roger Smith 2021-12-18

Verify that the function $y = e^{- 3 x}$ is a solution to the differential equation $d^{2} \frac{y}{{d x}^{2}} + \frac{d y}{d x} - 6 y = 0$ ?

William Burnett 2021-12-17

Solve the following linear differential equation $y^{6} - 64 y = 0$

Jason Yuhas 2021-12-17

A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?

Hello,

i'm here because i didn't found anything general on this topic, i need to know what is the expression of the laplace transform a composed function like that : $L {f (x) \circ g (x)} = L {f (g (x))} = ? ?$

my complete equation to transform is : $x (t) = 4 \times [\ddot{a} (t) c o s (a (t)) - \dot{a} (t)^{2} s i n (a (t))] + 2500 y (t) = 4 \times [- \ddot{a} (t) s i n (a (t)) - \dot{a} (t)^{2} c o s (a (t))] + \frac{3.711}{4} \times t^{2} + 2700$

the goal is to isolate the $a (t)$ function as a function of $x (t)$ and $y (x)$

Thanks for your time,

Robin Luiz

PEEWSRIGWETRYqx 2021-12-16

Solve the given LDE: $y^{6} - 64 y = 0$

crealolobk 2021-12-16

Apply unknown coefficients to the following differential equation to solve it.
$y^{″} + 7 y^{'} + 6 y = 30$

Zerrilloh6 2021-12-16

$d 2 \frac{x}{d t} 2 + 4 \frac{d x}{d t} + 4 x = 0$
$x (0) = 2, x^{'} (0) = 1$

Joseph Krupa 2021-12-12

Find $\frac{d y}{d x}$ and $\frac{d^{2} y}{{d x}^{2}} . x = e^{t}, y = t e^{- t}$ For which values of t is the curve concave upward?

Patricia Crane 2021-12-11

Find the Laplace transform of
$f (t) = 10 e^{- 200 t} u (t)$
Would it be correct to take out the 10 because it is a constant, find the Laplace transform of $e^{- 200 t}$ and then multiply it by the Laplace transform of u(t) to obtain a final answer of
$10 (\frac{1}{s + 200}) (\frac{1}{s})$
The u(t) is what is really confusing me in this problem.

Deragz 2021-12-11

Using the Laplace Transform Table in the textbook and Laplace Transform Properties,find the (unilateral) Laplace Transforms of the following functions:
$t \cos (ω_{0} t) u (t)$

Marla Payton 2021-12-11

Evaluate this laplace transform of $\frac{1 - e^{- t}}{t}$ and the integral exists according to wolfram

Stacie Worsley 2021-12-11

I'm having trouble with the laplace transform: $L {\sqrt{\frac{t}{π}} \cos (2 t)}$
The problem gives me the transform identity $L {\frac{\cos (2 t)}{\sqrt{π t}}} = \frac{e^{- \frac{2}{s}}}{\sqrt{s}}$ but i'm not sure/confused as to why that would help me

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