Solve the homogeneous equations. First put the equation in the form of a homogeneous equation. (x +
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Solve the homogeneous equations. First put the equation in the form of a homogeneous equation.
(x + y) dy + (x - y) dx = 0
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A first-order differential equation of the form dy dx is called homogeneous. It can be transformed into an equation whose variables are separable by defining the new variable v = y/x. Then, y = vx and dy dx dx du + = v + x² Substitution into the original differential equation and collecting terms with like variables then gives the separable equation dx dv v - F(v) 0. After solving this separable equation, the solution of the original equation is obtained when we replace v by y/x.
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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