Solve the following differential equation using Laplace transform, d²y dy dx 尝- dy dx +10y = e2x+20, knowing that when x = 0, y= 0 and dx? then substitute a, b, and c with numerical values in the solution below, 5x e 3 2x y = a+ - 3 3 a= b= C= 1/3

Q: te √e³x Evaluate 3x cos 4x dx.

A:

Q: Evaluate Se²x 2x Se²x 2x cos (5x) dx. cos (5x) dx = e2x. (5 sin (5x) + 2 cos (5x)) 19 + C

A:

Q: By expressing the product as a sum, 2cos(3x)cos(4x)= ?

A:

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

A:

Q: v = ) V In(2x-3y

A:

Q: What would the inverse Laplace Transform be for the attached function if A = 1+j4 and B = 3+j7?…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find all the solutions to sinh(z) = i/2

A: Solutions are:z=i(1+12k)6π​,k∈Zandz=i(5+12k)6π​,k∈ZExplanation:Step 1:Step 2: Step 3: Step 4:

Q: 3x'y"+2xy' = 0 %3D

A:

Q: A/ 10 Evaluate 4/1+ cos 10x dx. A/ 10 4/1+ cos 10x dx =

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.