Answer to Question #149408 in Differential Equations for Cristine

Question

Solve the initial value problem
y"+y=0 y(0)=2 y'(0)=0

Answer 1

"y"+y=0,\\,\\, y(0)=2,\\,\\, y'(0)=0\\\\\n\n\\textsf{The auxiliary equation is}\\\\\n\nm^2 + 1 = 0, m^2 = -1\\\\\n\nm = \\pm\\sqrt{-1} = \\pm j\\\\\n\n\n\\textsf{The general solution to the}\\\\ \\textsf{differential equation is}\\\\\n\ny = B\\cos{x} + C\\sin{x}\\\\\n\n\ny(0) = B = 2, \\therefore B = 2.\\\\\n\n\ny' = -B\\sin{x} + C\\cos{x}\\\\\n\n\ny'(0) = C = 0\\\\\n\n\n\\therefore \\textsf{The particular solution is}\\\\\n\n\ny = 2\\cos{x}"