Solve y′′−100y′+2500y=0y'' - 100y' + 2500y = 0y′′−100y′+2500y=0.
y=Ce50xy = C e^{50x}y=Ce50x
y=C1e50x+C2e−50xy = C_1 e^{50x} + C_2 e^{-50x}y=C1e50x+C2e−50x
y=(C1+C2x)e50xy = (C_1 + C_2 x)e^{50x}y=(C1+C2x)e50x
y=C1cos(50x)+C2sin(50x)y = C_1 \\cos(50x) + C_2 \\sin(50x)y=C1cos(50x)+C2sin(50x)