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Show that the substitution v= ax + by + c transforms the differential equation A first-order differential equation is called separable provided that f(x,y) can be written as If v = ax +by+c, then = dv dx ▼ dy Thus, for the substitution v = ax +by+c, = dx dy dx = F(ax + by + c) into a separable equation. ▼ dy Substitute v and in the given differential equation = F(ax + by + c) to get dx dy dx Rearrange the equation found in the previous step to isolate the v and x terms. The rearranged equation is ▼ AWE =dx. This is a separable equation.

Show that the substitution v= ax + by + c transforms the differential equation A first-order differential equation is called separable provided that f(x,y) can be written as If v = ax +by+c, then = dv dx ▼ dy Thus, for the substitution v = ax +by+c, = dx dy dx = F(ax + by + c) into a separable equation. ▼ dy Substitute v and in the given differential equation = F(ax + by + c) to get dx dy dx Rearrange the equation found in the previous step to isolate the v and x terms. The rearranged equation is ▼ AWE =dx. This is a separable equation.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Show that the substitution v= ax + by + c transforms the differential equation A first-order differential equation is called separable provided that f(x,y) can be written as If v = ax +by+c, then dv dx 11 Thus, for the substitution v= ax + by + c, dy dx dy -= = F(ax + by + c) into a separable equation. dx Pa dy dy Substitute v and in the given differential equation = F(ax + by + c) to get dx dx ▼ Rearrange the equation found in the previous step to isolate the v and x terms. The rearranged equation is wa1 =dx. This is a separable equation.
Transcribed Image Text:Show that the substitution v= ax + by + c transforms the differential equation A first-order differential equation is called separable provided that f(x,y) can be written as If v = ax +by+c, then dv dx 11 Thus, for the substitution v= ax + by + c, dy dx dy -= = F(ax + by + c) into a separable equation. dx Pa dy dy Substitute v and in the given differential equation = F(ax + by + c) to get dx dx ▼ Rearrange the equation found in the previous step to isolate the v and x terms. The rearranged equation is wa1 =dx. This is a separable equation.
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