Consider the differential equation dy dx = 3y 2x

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Consider the differential equation dydx=3y2x,x>0,\frac{dy}{dx}=\frac{3y}{2x},\qquad x>0, and the student work shown below attempting to verify that y=kx3/2y=k x^{3/2} is a solution. Student work (with one error): (a) Identify the specific step in the student work that fails to justify the conclusion and clearly describe the error. (b) Provide a complete and correct verification that y=kx3/2y=k x^{3/2} satisfies the differential equation for x>0x>0. (c) Explain why the condition x>0x>0 is essential for the verification in part (b).

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