Differential Equations Quiz
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FIRST-ORDER DIFFERENTIAL EQUATIONS
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A student is solving the equation xy′=2x+yx y' = 2x + y. They correctly identify it as a homogeneous equation and apply the substitution y=vxy=vx. However, they make a common error in the substitution for y′y', replacing it with xdvdxx\frac{dv}{dx} instead of the correct v+xdvdxv+x\frac{dv}{dx}. Following this incorrect procedure, what general solution do they obtain?
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