The initial-value is
x(t)=F0/2w^2 (sin wt-wt cos wt)
An initial-value hassle is a differential equation wherein is an open set of, together with a point within the domain called the initial situation. A technique to an initial cost hassle is a function that is a technique to the differential equation and satisfies.
Inside the discipline of differential equations, preliminary cost trouble (additionally called Cauchy trouble by using a few authors) is a normal differential equation collectively with a detailed fee, called the preliminary situation, of the unknown function at a given factor in the domain of the solution.
In multivariable calculus, an initial-value hassle is a normal differential equation collectively with a preliminary circumstance that specifies the fee of the unknown characteristic at a given factor in the area. Modeling a system in physics or different sciences often amounts to fixing an initial cost problem.
Consider a differential equation x+x=F, sin wt, x(0) = 0,X(0) = 0
Apply Laplace transformation on both sides, and we get
(s²L{x(t)}-sy(0)-y'(0)) + w²L {x(t)} =·
Fow
Fow
(s² + w² ) { x(t)} = 3 + w²
L{x(t)}=
Fow
(5²+w²)²
x(t)=FwL
[(s² + w²)²]
Fow
x(t)=(sin wt-wt coswt)
2w
x(t)=
Fo
wtcos
2w (sin wt-wt cos wt),
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