section%202.5 - Chapter 2 First Order Dierential Equations...

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Chapter 2. First Order Differential Equations § 2.5 Solutions by Substitutions 1. Homogeneous functions and homogeneous equations: If a function f ( x, y ) possesses the property f ( tx, ty ) = t α f ( x, y ) for some real number α , then f is said to be a homogeneous function of degree α. A first order differential equation of the form M ( x, y ) dx + N ( x, y ) dy = 0 is said to be a homogeneous if both M and N are homogeneous of the same degree. To solve an homogeneous equation, use the substitution y = ux or x = vy to reduce the equation to a separable DE. EX: Solve the following DEs.
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