find a general solution for the following bessel s differential equati

Question

Find a general solution for the following Bessel's differential equations in terms of J, and Y, (or J). Use the indicated transformation. The details of the derivations should be provided. \text { 1. } x y^{\prime \prime}+3 y^{\prime}+x y=0,(y=u / x) \text {. } \text { 2. } 9 x^{2} y^{\prime \prime}+9 x y^{\prime}+\left(9 x^{4}-4\right) y=0,\left(z=x^{2} / 2\right) \text {. } \text { 3. } 4 x y^{\prime \prime}+4 y^{\prime}+y=0,(\sqrt{x}=z) \text {. } \text { 4. } x y^{\prime \prime}+y^{\prime}+4 y=0,(z=4 \sqrt{x}) \text {. } \text { 5. } x y^{\prime \prime}-3 y^{\prime}+x y=0,\left(y=x^{2} u\right) \text {. }