Use Laplace transforms to solve the following differential equation: y" – y' + y = t given y(0) = y'(0) = 1.

Q: Form the differential equation for the function y = acos(2x + b)

A: By finding first and second derivatives of function we form the required differential equation as…

Q: y = C, x? sin 4x + C2x² Cos 4x

A: The equation is y = C1x2sin4x+C2x2cos4x

Q: Find the slopes given by the differential equation y'= y-2 at each of the following points: a. (0,0)…

A:

Q: Calculate the increment and differential of the function y=x+2/x+1 at the point x=0 when Δx=0,1.

A: The increment of the function: y=f(x) is calculated using the formula: ∆y=fx+∆x-f(x). The…

Q: Sketch the direction or slope field of the differential equation. Be sure to show any “trends" and…

A: Given differential equation is y'=x-2y+1                   (i) Direction field of the given eq. (i)…

Q: se variation of parameters to solve the given differential equation y" + y = tan:

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.