A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?
Answer: y = vx, dy = vdx + xdv
Explanation
- The correct answer is: y = vx, dy = vdx + xdv
- This substitution is used to solve homogeneous differential equations, as it allows for the separation of variables.
- By substituting y = vx and dy = vdx + xdv, the original equation can be transformed into a separable equation, which can then be solved by integrating both sides separately.
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