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

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Find the general solution of the differential equation dydx=e(x)+2xx+5y2+1\frac{dy}{dx}=\frac{e^{(x)}+2*x-\sqrt{x+5}}{y^2+1}.

A

y3+y=e(x)+x223(x+5)3/2+Cy^3+y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C

B

y33y=e(x)+x223(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)+x223(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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