Laplace transforms periods
If f(t) is a period, continuous function with period T>0, show that its Laplace transformation is... (See attachment for full question)
Calculus and Analysis
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Differential Equation and a Spring
I am looking for a detailed solution. I need set up, solving, and final result. Therefore, I need solution of the second order DFQ. Finally for the description of the movement as time goes to infinity, I need what type of motion is that. a. An 8lb weight is attached to a spring suspended from the ceiling. When the weight come
Modelling and Simulation
Please see the attached file the Modelling and Simulation
Differential equation explanation
I need to know how to find a particular solutions to an initial conditions. i know how to find the explicit solution of a differential equation but cannot remember how to find particular solutions. please show your working to help me understand. thanks Problems (also attached): Given the attached information: 1) So how
Initial-Value Problem : Solve with Laplace Transformations
Using Laplace transformations solve the Initial Value Prblem: y"-2y'+10y=1 y(0)=1 y'(0)=2 For the solution please use laplace transformations and partial fractions.
Initial-Value Problem involving Graph, Lapace Transformations
Solve the Initial Value Problem where g(t) is the function graphed and it is attached to this problem. Solve the following differential equation: y"-3y'+2y=g(t) y(0)=1 y'(0)=0
Initial value problem//Involving Laplace transformations
A) Solve the Initial value Problem: y"+y=dπ(t)+d2π(t)+d3π(t)+......dnπ(t) ******dπ.- meaning delta sub index phi******** b) Graph the solution on the interval [0,3π] c) Discuss the behaviour of the solution in relation to the equation. I am looking for a solution for this problem. I need the solution to be very espl
Implicit Differential Equations and Explicit Form of Solution
I) Find in implicit form, the general solution of the differential equation: dy/dx = 12y^(4/3)sin x cos^5 x (y > 0) ii) Find the corresponding explicit form of this solution. See the attached file.
Solve and Explain Three Integrals
∫ (x^5)/[(1+x^3)^(3/2)] dx ∫ {square root of [(x+3)/(x+1)]}dx ∫ (cot^3 v)[(csc v)^(3/2)] dx (I will use the $ sign for the integral sign) Problem #1: $ (x^5)/[(1+x^3)^(3/2)] dx the power 3/2 in the denominator is throwing me off greatly, as is the greater power (x^5) in the numerator. attempt 1
Even, Odd, and Periodic Fuctions : Periodicity and Fundamental Period
Determine whether or not the given function is periodic. Find the fundamental period. (h) sinh x (q) cos(sin x) Please see the attached file for the fully formatted problems.
Damping and Resonance Problem : Forces and Displacement
A seismograph is a scientific instrument that is used to detect earthquakes. A simple model of a seismograph is shown below. It consists of a particle of mass m to which a pointer is attached. The particle is suspended by a spring of natural length lo and stiffness k and a damper of damping constant r from a platform of height d
Related Rates : Find the rate of increase in the height of a cone.
Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high?
Evaluating the Integral with Limits
Please could you solve the following question showing every stage as simply as possible to get to the correct answer. Where any calculus rules are used could you please explain. Integrate sec^2(3t) - cosec^2(5t) between the limits t = 0 and t = pi/4 Please see attached for a more clear version.
Second order Diferential equation with Wronskian
Let y1, y2 be twice differentiable functions on an interval (a,b) whose Wronskian is nowhere zero. Show that there... Please see attached.
Statements about Differential Equations
I am looking for the best statements about solutions and how is the statement supported... Please see attached.
Differential Equations: Second Order
Find general solution of a second order differential equation. See the attached file.
Graphical methods
Ref. M4. use graphical methods to find the differential coefficient of simple sinusoidal and exponential functions. Please help with correct steps and formulas to get answer. Please see attachment
Find the dimensions of the rectangle of area A sq. units that has the smallest perimeter.
I am in Freshmen Level Calculus. We are in section 4.5 of the Salas, Hille, and Etgen book, "Calculus: One and Several Variables" 9th edition. The name of the chapter is The Mean value theorem and its applications, But from my understanding of the examples, It does not use the MVT. The previous sections were about local ex
Largest possible area for a rectangle bordered by the x-axis
I am in Freshmen Level Calculus. We are in section 4.5 of the Salas, Hille, and Etgen book, "Calculus: One and Several Variables" 9th edition. The name of the chapter is The Mean value theorem and its applications, But from my understanding of the examples, It does not use the MVT. The previous sections were about local extre
Inverse Function Equations
Find the equation of the attached inverse function, if the function is invertible.
Vertex and intercepts
Find the vertex and intercepts for the quadratic function and sketch its graph y=x^2+4x
Horizontal asymptote
The function N(t) = (0.8t + 1000 ) / (5t+4), where t=>15 gives the body concentration N(t), in parts per million, of a certain dosage of medication after time t, in hours. ? Find the horizontal asymptote of the graph and complete the following statement: N(t) approaches ? as t approaches infinity.
Solving the Given Integral
Solve: 2pi/(x^2+1).
Differential equation solved
Solve t^2y''+3ty'+5y=0
Boundary Value Problem : Separation of Variables and Laplace's Equation
Solution of Laplace's Equation 4. Using separation of variables solve the following boundary value problem... Please see the attached file for the fully formatted problem.
Differential Equations and Variation of Parameters
Solve t^2y''+ty'-y=2t^2 sin t t not equal to zero Use method of variation of parameters Solve ∫t^2 sin t dt= -t^2 cos t + 2t sin t +2 cos t
Differential Equations for Initial condition Changes
I am currently having trouble with some of this stuff, and my job requires that i learn this all again so i was wondering if i could get some help t(t-3)y''+2ty'-y=t^2 y(1)=yo, y'(1)=y1 y1 and yo are real constants find the interval of the unique solution Also find the interval if the above initial condition changes to y(
Differential Equations : LaPlace Tranform Method
Use the LaPlace transform method to solve the initial-value problem y'''+y''-2y'+y=cos2t, y(0)=1, y'(0)=0, y''(0)=-1 Please show all work! Thanks
Differential Equations : Variation of Parameters
Use variation of parameters to solve the differential equation y'''+4y'=cot2t.
Linear PDE, Order, Homogeneous, Non-Homogeneous : Boundary Value Problems
A linear PDE can be written in differential operator notation L(u) = f. where L is the linear differential operator, u is the unknown function, and f is the right-hand side function. For each of the following PDEs, determine the linear operator and the right-hand side function, the order of the PDE, and whether the PDE is homog