Engineering Board Exam Reviewer · Homogeneous First-Order Equations · easy

Which substitution reduces a homogeneous first-order differential equation to a separable one?

1. y=vx
2. y=v+x
3. y=evx
4. y=v/x

Answer

A. y=vx

Solution

For dy/dx=f!≤ft( yx ), set y=vx. Then dy/dx=v+xdv/dx and the variables v and x separate.

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