Let M(x,y) = x+y-3 and N(x,y) = x+3y-7. 1. Find α, β ∈ R such that if u=x-α and v=y-β, then M((x(u), y(v)) and N((x(u), y(v)) become homogenous (i.e each takes the form γu + δv). 2. Use the above substitution to solve the particular solution to M(x,y)dx + N(x,y)dy =0 which passes through (2,2)

Let M(x,y) = x+y-3 and N(x,y) = x+3y-7. 1. Find α, β ∈ R such that if u=x-α and v=y-β, then M((x(u), y(v)) and N((x(u), y(v)) become homogenous (i.e each takes the form γu + δv). 2. Use the above substitution to solve the particular solution to M(x,y)dx + N(x,y)dy =0 which passes through (2,2)

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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