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In this problem we consider an equation in differential form M dx + Ndy = 0. The equation in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have (3e - (8xy²e +2e=ªsin(x))) da + (− (8x²yeª +3e"))dy:

In this problem we consider an equation in differential form M dx + Ndy = 0. The equation in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have (3e - (8xy²e +2e=ªsin(x))) da + (− (8x²yeª +3e"))dy:

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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In this problem we consider an equation in differential form M dx + Ndy = 0. The equation in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of alone since can be considered as a function of a alone. Namely we have μ(x) = e^x Multiplying the original equation by the integrating factor we obtain a new equation M da + Ndy = 0 where M = -8xY^2+3e^(x-y)-2sin(x) N = Which is exact since (3e (8xy²e +2e=ª sin(x))) dx + (− (8x²yeª + 3e¯¹))dy = 0 My = N₂ = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F'(x, y) = C where F(x, y) = M,-Ñz = M-N Ñ -8e^(-x)x^2y-3e^(-y) 1
Transcribed Image Text:In this problem we consider an equation in differential form M dx + Ndy = 0. The equation in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of alone since can be considered as a function of a alone. Namely we have μ(x) = e^x Multiplying the original equation by the integrating factor we obtain a new equation M da + Ndy = 0 where M = -8xY^2+3e^(x-y)-2sin(x) N = Which is exact since (3e (8xy²e +2e=ª sin(x))) dx + (− (8x²yeª + 3e¯¹))dy = 0 My = N₂ = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F'(x, y) = C where F(x, y) = M,-Ñz = M-N Ñ -8e^(-x)x^2y-3e^(-y) 1
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