Use Euler's method to integrate: y'=5x²-0.5y from x=0 to x=7 with a step size of 1. The initial condition at x = 0 is y = 4. The solution of the given equation at x = 7 is:
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- Find the inverse laplace transform of the following function, complete all work by hand.h = 0.25 solve for the differential equation y (1) h take and calculate approximately with Euler's method.Suppose a spring with spring constant k=1 supports a mass of 1kg and is subject to a driving force f(t)=sin2t. The mass is initially at rest at its equilibrium point. At time t=2, the mass is hit with a sharp upward blow, so that the force of the blow is δ(t−2). Set up and solve (using Laplace transforms) an initial-value problem modelling this situation.
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