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AP Calculus AB/Unit 7: Differential Equations
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Solving a Separable Differential Equation

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What is the general solution to the differential equation dydx=ex+2x−x+5y2+1\frac{dy}{dx}=\frac{e^x+2x-\sqrt{x+5}}{y^2+1}?

A

y3+y=e(x)+x2−23(x+5)3/2+Cy^3+y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C

B

y33−y=e(x)+x2−23(x+5)3/2+C\frac{y^3}{3}-y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C

C

y33+y=e(x)+x2−23(x+5)3/2+C\frac{y^3}{3}+y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C

D

y33+y=e(x)+x2+23(x+5)3/2+C\frac{y^3}{3}+y=e^{(x)}+x^2+\frac{2}{3}(x+5)^{3/2}+C

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