(a) By inspection find a one-parameter family of solutions of the differential equation xy ′ = y . Verify that each member of the family is a solution of the initial-value problem xy ′ = y, y (0) = 0. (b) Explain part (a) by determining a region R in the xy -plane for which the differential equation xy ′ = y would have a unique solution through a point ( x 0 , y 0 ) in R . (c) Verify that the piecewise-defined function y = { 0 , x < 0 x , x ≥ 0
(a) By inspection find a one-parameter family of solutions of the differential equation xy ′ = y . Verify that each member of the family is a solution of the initial-value problem xy ′ = y, y (0) = 0. (b) Explain part (a) by determining a region R in the xy -plane for which the differential equation xy ′ = y would have a unique solution through a point ( x 0 , y 0 ) in R . (c) Verify that the piecewise-defined function y = { 0 , x < 0 x , x ≥ 0
(a) By inspection find a one-parameter family of solutions of the differential equation xy′ = y. Verify that each member of the family is a solution of the initial-value problem xy′ = y, y(0) = 0.
(b) Explain part (a) by determining a region R in the xy-plane for which the differential equation xy′ = y would have a unique solution through a point (x0, y0) in R.
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
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