Infinite Series Method 2nd order DE

The following second order Differential Equations must be solved with the appropriate Infinite Series Method. You may verify DE with other method only after work is shown step by step using the infinite series methods. Problems Use appropriate infinite series method about x=0 to find solutions of the given DE. 1) xy"- ...continues

Solving differential equations with the Laplace Transform

Use Laplace Transforms to solve problems below. Please show all work step by step I am using your work as a study guide for my upcoming Final, so please explain well. Scannned work is ok as long as I can read it. Use Laplace Transforms to solve DE's. 1) y" - 8y' + 20y = t(e^t) , y(0)=0 , y'(0)=0 2) y''' + 2y ...continues

Modeling with Higher Order Differential Equations

Two springs are attached in series as shown in Figure 5.42. If the mass of each spring is ignored, show that the effective spring constant k ot the system is defined by I/k = I/k + I/k2. A mass weighing W pounds stretches a spring 1/2 foot and stretches a different spring 1/4 foot. The two springs are attached, and the mass is ...continues

Laplace Transform

(See attached file for full problem description)

Linear differential operator

Problem states " if L[y] =ay'' +by' +cy, where a,b,and c are constants, compute L[e^rx], where "r" is constant. Is this just a matter of substituting for "y"? Please work out, thanks!

Substituting variable

Please show how to solve y’’ – 3y^2=0, substituting v=y’ so y’’ = v dv/dy Initial conditions are y(0) =2 and y’(0)=4 I got it as far as dy/dx = (y^3 +c)^1/2 but that might be wrong!

Laplace Transforms

Please show work by step by step. Scanned work is OK as long as I can read it.

Laplace Transforms

Please show all work step by step. Scanned work is OK as long as I can read it. Two problems attached please complete both.

Matrices

These are problems from the text that were advised to study for the next exam. (see attachment for equations) 1) Determine the values of r for which det(A-rI) = 0 2) Verify that X(t) is a fundamental matrix for the given system and compute X-1(t). Use the result, x’ = Ax, x(t0) = x0 to find the solution to t ...continues

Substitution of "v" in a 2nd order d.e.

I have been tasked with solving y’’ – 3y^2 =0 using the technique used substituting v for y’, therefore substituting v dv/dy for y’’. (Equation with “x” missing) I broke it down as follows Y’’ -3y^2 =0 Y’’ =3y^2 Substituting I get v dv/dy = 3y^2 Separating variables, I get v dv =3y^2dy Integrating I get 1/2v^2 +c = y^3 +c ...continues