(Solved): Solve the given first order, linear DE by the method of integrating factor. Select the correct pai ...

Solve the given first order, linear DE by the method of integrating factor. Select the correct pair of the integrating factor and general solution from the options below. \[ \left(x^{2}+3\right) y^{\prime}+2 x y=5 x^{2}\left(x^{2}+3\right) \] \[ \begin{array}{l} \mu=x^{2}+3 \\ y=\frac{5 x^{3}+C}{3\left(x^{2}+3\right)} \end{array} \] \[ \begin{array}{l} \mu=x^{2}+3 \\ y=\frac{x^{5}+5 x^{3}+C}{x^{2}+3} \end{array} \] \[ \begin{array}{l} \mu=e^{2 x} \\ y=\frac{5}{2} x^{2} e^{2 x}-\frac{5}{2} x e^{2 x}+\frac{5}{4} e^{2 x}+C \end{array} \] \[ \begin{array}{l} \mu=e^{\ln \left(x^{2}+3\right)} \\ y=10 x e^{\ln \left(x^{2}+3\right)}+\frac{10 x^{3}}{x^{2}+3} e^{\ln \left(x^{2}+3\right)}+C \end{array} \]