APFIVE Solving a Separable Differential Equation
What is the general solution to the differential equation $$\frac{dy}{dx}=\frac{e^x+2x-\sqrt{x+5}}{y^2+1}$$?
A
$$y^3+y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C$$
B
$$\frac{y^3}{3}-y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C$$
C
$$\frac{y^3}{3}+y=e^{(x)}+x^2+\frac{2}{3}(x+5)^{3/2}+C$$
D
$$\frac{y^3}{3}+y=e^{(x)}+x^2-\frac{2}{3}(x+5)^{3/2}+C$$
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