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39. (a) Show that a one-parameter family of solutions of the equation 102 (4xy + 3x²) dx + (2y + 2x²) dy = 0 is x³ + 2x²y + y² = c. (b) Show that the initial conditions y(0) = -2 and y(1) = 1 determine the same implicit solution. (c) Find explicit solutions y₁(x) and y₂(x) of the differential equation in part (a) such that y₁ (0) = -2 and y₂(1) = 1.

39. (a) Show that a one-parameter family of solutions of the equation 102 (4xy + 3x²) dx + (2y + 2x²) dy = 0 is x³ + 2x²y + y² = c. (b) Show that the initial conditions y(0) = -2 and y(1) = 1 determine the same implicit solution. (c) Find explicit solutions y₁(x) and y₂(x) of the differential equation in part (a) such that y₁ (0) = -2 and y₂(1) = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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d 39. (a) Show that a one-parameter family of solutions of the equation (b) (4xy + 3x²) dx + (2y + 2x²) dy = 0 is x² + 2x²y + y² = c. Show that the initial conditions y(0) = -2 and y(1) = 1 determine the same implicit solution. (c) Find explicit solutions y₁(x) and y2(x) of the differential equation in part (a) such that y₁ (0) = -2 and y₂(1) = 1.
Transcribed Image Text:d 39. (a) Show that a one-parameter family of solutions of the equation (b) (4xy + 3x²) dx + (2y + 2x²) dy = 0 is x² + 2x²y + y² = c. Show that the initial conditions y(0) = -2 and y(1) = 1 determine the same implicit solution. (c) Find explicit solutions y₁(x) and y2(x) of the differential equation in part (a) such that y₁ (0) = -2 and y₂(1) = 1.
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