Consider the differential equation:

2y'' + ty' ? 2y = 14, y(0) = y'(0) = 0.

In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1., THEOREM 7.4.1 Derivatives of Transforms If F(s) = ${f(t)} and n = 1,2, 3, . . . , then nd" d5" ${t"f(t)} = (-1) F(S), to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = ${y(t)}