Can you walk me through the problem: Use the Laplace transform to solve the following initial value problem:y″+4y′−21y=0 y(0)=-1, y′(0)=2. First, using Y for the Laplace transform of y(t), i.e., Y={y(t)}, find the equation you get by taking the Laplace transform of the differential equation. Now solve for Y(s). And write the above answer in its partial fraction decomposition, Y(s)=A/(s+a)+B/(s+b) where a<b. Now by inverting the transform, find y(t).
Can you walk me through the problem: Use the Laplace transform to solve the following initial value
problem:y″+4y′−21y=0 y(0)=-1, y′(0)=2. First, using Y for the Laplace transform of y(t), i.e., Y={y(t)}, find the equation you get by taking the Laplace transform of the differential equation. Now solve for Y(s). And write the above answer in its partial fraction decomposition, Y(s)=A/(s+a)+B/(s+b) where a<b. Now by inverting the transform, find y(t).
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