Laplace transforms and applications
Engineering Mathematics · Engineering
Study notes
Solve y'' + y = 0, y(0)=0, y'(0)=1 using Laplace transforms. Take L: s²Y − sy(0) − y'(0) + Y = 0 → (s²+1)Y = 1. Y = 1/(s²+1). Inverse Laplace: y = sin(t). ✓ Check: y'' = −sin t, so y'' + y = 0 ✓