Question

In the given equation , solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form M(x, y) dx +N(x, y) dy = 0 where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions y = vx and dy = x dv + v dx. xy dx + ( y2 - x2 ) dy = 0

Name: in the given equation solve the homogeneous differential equation in terms of x and y a homogeneous differential equation is an equation of the form mx y dx nx y dy 0 where m and n are homog 68388
Uploaded: 2023-02-18T16:05:10-08:00
Duration: 2 min 42 s
Channel: Adi S
Description: in the given equation solve the homogeneous differential equation in terms of x and y a homogeneous differential equation is an equation of the form mx y dx nx y dy 0 where m and n are homog 68388

          In the given equation , solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an
equation of the form
M(x, y) dx +N(x, y) dy = 0
where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions y = vx and dy = x dv + v dx.
xy dx + ( y2 - x2 ) dy = 0

Added by Jennifer J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

02/18/2023

Step 1

M(x, y) = -2x + y N(x, y) = 2x + y Now we can use the substitution y = vx to solve for x. x = vx + 2v Show more…

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In the given equation , solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form M(x, y) dx +N(x, y) dy = 0 where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions y = vx and dy = x dv + v dx. xy dx + ( y2 - x2 ) dy = 0