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)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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