Show that the differential equation °y"+ a(1+y)y 0 is not exact, but becomes exact when multiplied by the integrating factor %3D H(t, y) = 1 Then solve the equation. %3D xy7 The given equation is not exact, because My %3D which is different from N %3D After multiplication with u(z,y), the equation is exact, because then My = N = %3D %3D The general solution of the differential equation is given implicitly by c, for any constant c, where y > 0. %3D
Show that the differential equation °y"+ a(1+y)y 0 is not exact, but becomes exact when multiplied by the integrating factor %3D H(t, y) = 1 Then solve the equation. %3D xy7 The given equation is not exact, because My %3D which is different from N %3D After multiplication with u(z,y), the equation is exact, because then My = N = %3D %3D The general solution of the differential equation is given implicitly by c, for any constant c, where y > 0. %3D
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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Transcribed Image Text:Show that the differential equation °y"+ a(1+y)y 0 is not
exact, but becomes exact when multiplied by the integrating factor
%3D
H(t, y) =
1
Then solve the equation.
xy7
The given equation is not exact, because My=
%3D
which is different from N
%3D
After multiplication with u(z, y), the equation is exact, because then
My = N, =
%3D
%3D
The general solution of the differential equation is given implicitly by
for
any constant c, where y > 0.
C,
%3D
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