1.

Solve this Differential Equation to find its General Solution.\((x+3)\frac{d^2y}{dx^2}+2 \frac{dy}{dx}+\frac{y}{(x+3)}=4\)

A. \(\frac{4x}{3}+2+\frac{1}{(x+3)}×c_1cos⁡(\frac{\sqrt{3}}{2} log⁡(x+3))+c_2sin⁡(\frac{\sqrt{3}}{2} log⁡(x+3))\)
B. \(\frac{4x}{3}+4+\frac{1}{(x+3)}×c_1cos⁡(\frac{\sqrt{3}}{2} log⁡(x+3))+c_2sin⁡(\frac{\sqrt{3}}{2} log⁡(x+3))\)
C. \(x+4+\frac{1}{(x+3)}×c_1cos⁡(\frac{\sqrt{3}}{2} log⁡(x+3))+c_2sin⁡(\frac{\sqrt{3}}{2} log⁡(x+3))\)
D. \(\frac{2x}{3}+4+\frac{1}{(x+3)}×c_1cos⁡(\frac{\sqrt{3}}{2} log⁡(x+3))+c_2sin⁡(\frac{\sqrt{3}}{2} log⁡(x+3))\)
Answer» C. \(x+4+\frac{1}{(x+3)}×c_1cos⁡(\frac{\sqrt{3}}{2} log⁡(x+3))+c_2sin⁡(\frac{\sqrt{3}}{2} log⁡(x+3))\)


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