These properties are of practical and theoretical importance because they enable us to obtain new solutions from
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These properties are of practical and theoretical importance because they enable us to obtain new solutions from given ones. Thus in modeling, whenever possible, we prefer linear ODEs over nonlinear ones, which have no similar properties.
Show that nonhomogeneous linear ODEs (1) and homogeneous linear ODEs (2) have the following properties. Illustrate each property by a calculation for two or three equations of your choice. Give proofs.
If y1 and y2 are solutions of y'1 + py1 = r1 and y'2 + py2 = r2, respectively (with the same p!), what can you say about the sum y1 + y2?
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The sum satisfies the ODE with r 1 r 2 on the right This is important a...View the full answer
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