APFIVE Solving a Separable Differential Equation
Solve the differential equation $$\frac{dy}{dx}=\frac{3*x+\sqrt{x+1}-\frac{1}{x}}{y}$$ with the initial condition $$y(1)=2$$. Express your answer in explicit form.
A
$$y(x)=\sqrt{3*x^2+\frac{4}{3}(x+1)^{3/2}+2\ln|x|+1-\frac{4\sqrt{2}}{3}}$$
B
$$y(x)=\sqrt{3*x^2-\frac{4}{3}(x+1)^{3/2}-2\ln|x|+1-\frac{4\sqrt{2}}{3}}$$
C
$$y(x)=\sqrt{3*x^2+\frac{4}{3}(x+1)^{3/2}-2\ln|x|+1-\frac{4\sqrt{2}}{3}}$$
D
$$y(x)=\sqrt{3*x^2+\frac{4}{3}(x+1)^{3/2}-2\ln|x|-1+\frac{4\sqrt{2}}{3}}$$
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