Question

Use the Laplace transform to solve the given initial-value problem.

y ′′+4y = cos(2t),y(0) = 3,y ′ (0) = 5
y(t ) = tsin(2t)/4+5cos(2t) + (3/2) sin(2t)
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Answer 1

This mathematics problem involves using the Laplace transform to find the solution to a differential equation, which is a topic often encountered in college-level mathematics or engineering courses.

Step-by-step explanation:

The subject of this question is the application of the Laplace transform to solve an initial-value problem in the realm of differential equations, which is a topic under mathematics. The grade level is college, as this type of problem typically appears in collegiate mathematics courses, particularly those focusing on differential equations and engineering mathematics. The process involves taking the Laplace transform of each term in the differential equation, applying initial conditions, and then using algebraic methods to solve for the Laplace transform of the unknown function. After obtaining this transform, the solution to the original differential equation is found by taking the inverse Laplace transform.