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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 For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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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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Calculus For The Life Sciences
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