28. Constant Multiples of Solutions. (a) Show that y = eis a solution of the linear equation (16) and y dy dy dx dx = x¹

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28 Constant Multiples Of Solutions A Show That Y Eis A Solution Of The Linear Equation 16 And Y Dy Dy Dx Dx X 1 (135.91 KiB) Viewed 29 times

28. Constant Multiples of Solutions. (a) Show that y = eis a solution of the linear equation (16) and y dy dy dx dx = x¹ is a solution of the nonlinear equation dy + y = 0, (17) (b) Show that for any constant C, the function Ce™ is a solution of equation (16), while Cx¹ is a solution of equation (17) only when C = 0 or 1. (c) Show that for any linear equation of the form dx + y² = 0. + P(x) y = 0, if y(x) is a solution, then for any constant C the function Cŷ(x) is also a solution.