Solving ODEs with Laplace transforms
General · Mathematics
Study notes
Q: Solve y''+y = 0, y(0) = 1, y'(0) = 0 via Laplace. L: s²Y-s(1)-0+Y = 0: (s²+1)Y = s. Y = s/(s²+1). L⁻¹: y = cos t! Check: y'' = -cos t: y''+y = 0 ✓; y(0) = 1 ✓, y'(0) = 0 ✓! (Initial conditions built in!)