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Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation can be rewritten as dy = (y/x) - 4 dx 1 – (y/x) • - (b). Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. (c). Replace y and dy/dx in the equation part (a) by the expressions from part (b) that involve v and do/dx. Show that the resulting differential equation of v is separable, and solve it. (d). Find the solution y(x) by replacing o by y/x in the solution in part (c).

Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation can be rewritten as dy = (y/x) - 4 dx 1 – (y/x) • - (b). Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. (c). Replace y and dy/dx in the equation part (a) by the expressions from part (b) that involve v and do/dx. Show that the resulting differential equation of v is separable, and solve it. (d). Find the solution y(x) by replacing o by y/x in the solution in part (c).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation can be rewritten as dy = (y/x) - 4 dx 1 – (y/x) • - (b). Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. (c). Replace y and dy/dx in the equation part (a) by the expressions from part (b) that involve v and do/dx. Show that the resulting differential equation of v is separable, and solve it. (d). Find the solution y(x) by replacing o by y/x in the solution in part (c).
Transcribed Image Text:Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation can be rewritten as dy = (y/x) - 4 dx 1 – (y/x) • - (b). Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. (c). Replace y and dy/dx in the equation part (a) by the expressions from part (b) that involve v and do/dx. Show that the resulting differential equation of v is separable, and solve it. (d). Find the solution y(x) by replacing o by y/x in the solution in part (c).
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