Recall that a First Order Differential Equation of the form dy/dx = f(x, y) is called Homogeneous, provided f(x, y) is a Homogeneous Function of Degree Zero, i.e., f(λx, λy) = f(x, y) for any λ, x, y. Such equations can be transformed into Separable Equations by introducing a new unknown function v so that y = xv and by expressing dy/dx in terms of x, v and dv/dx. Use this procedure to solve the homogeneous equation dy/dx = (x^2 + 3xy + y^2) / x^2 , x > 0, y > 0.
Recall that a First Order Differential Equation of the form dy/dx = f(x, y) is called Homogeneous, provided f(x, y) is a Homogeneous Function of Degree Zero, i.e., f(λx, λy) = f(x, y) for any λ, x, y. Such equations can be transformed into Separable Equations by introducing a new unknown function v so that y = xv and by expressing dy/dx in terms of x, v and dv/dx. Use this procedure to solve the homogeneous equation dy/dx = (x^2 + 3xy + y^2) / x^2 , x > 0, y > 0.
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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Recall that a First Order Differential Equation of the form
dy/dx = f(x, y)
is called Homogeneous, provided f(x, y) is a Homogeneous Function of Degree Zero, i.e.,
f(λx, λy) = f(x, y)
for any λ, x, y. Such equations can be transformed into Separable Equations by introducing a new unknown function v so that
y = xv
and by expressing dy/dx in terms of x, v and dv/dx.
Use this procedure to solve the homogeneous equation
dy/dx = (x^2 + 3xy + y^2) / x^2 , x > 0, y > 0.
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