\[ -f(x)+x^2 y^{(3)}(x)+\left (x^2+2\right ) y'(x)+4 x y''(x)+3 x y(x)=0 \] ✓ Mathematica : cpu = 7.01168 (sec), leaf count = 2582
\[\left \{\left \{y(x)\to J_0(x) c_1+2 Y_0(x) c_2+\frac {2 c_3 \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {x^2}{4}\right )}{x}+\frac {x J_0(x) \int _1^x \left (\frac {-16 J_1(K[1]) Y_0(K[1]){}^2 f(K[1]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[1]^2\right ) K[1]^3+16 J_0(K[1]) Y_0(K[1]) Y_1(K[1]) f(K[1]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[1]^2\right ) K[1]^3+18 J_2(K[1]) Y_0(K[1]){}^2 f(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-18 J_0(K[1]) Y_0(K[1]) Y_2(K[1]) f(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-9 J_1(K[1]) Y_0(K[1]){}^2 f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]+9 J_0(K[1]) Y_0(K[1]) Y_1(K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]-9 J_2(K[1]) Y_0(K[1]) Y_1(K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]+9 J_1(K[1]) Y_0(K[1]) Y_2(K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]+36 J_1(K[1]) Y_0(K[1]){}^2 f(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]-36 J_0(K[1]) Y_0(K[1]) Y_1(K[1]) f(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]+9 J_2(K[1]) Y_0(K[1]){}^2 f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )+36 J_0(K[1]) Y_1(K[1]){}^2 f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )-36 J_1(K[1]) Y_0(K[1]) Y_1(K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )-9 J_0(K[1]) Y_0(K[1]) Y_2(K[1]) f(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )}{2 (J_0(K[1]) Y_1(K[1])-J_1(K[1]) Y_0(K[1])) \left (16 J_1(K[1]) Y_0(K[1]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[1]^2\right ) K[1]^4-16 J_0(K[1]) Y_1(K[1]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[1]^2\right ) K[1]^4-18 J_2(K[1]) Y_0(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^3+18 J_0(K[1]) Y_2(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^3+9 J_1(K[1]) Y_0(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-9 J_0(K[1]) Y_1(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2+9 J_2(K[1]) Y_1(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-9 J_1(K[1]) Y_2(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2+36 J_1(K[1]) Y_0(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-36 J_0(K[1]) Y_1(K[1]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[1]^2\right ) K[1]^2-9 J_2(K[1]) Y_0(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]+9 J_0(K[1]) Y_2(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right ) K[1]+36 J_1(K[1]) Y_0(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )-36 J_0(K[1]) Y_1(K[1]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[1]^2\right )\right )}-\frac {Y_0(K[1]) f(K[1])}{2 (J_1(K[1]) Y_0(K[1])-J_0(K[1]) Y_1(K[1])) K[1]}\right ) \, dK[1]+2 x Y_0(x) \int _1^x \left (\frac {16 J_0(K[2]) J_1(K[2]) Y_0(K[2]) f(K[2]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[2]^2\right ) K[2]^3-16 J_0(K[2]){}^2 Y_1(K[2]) f(K[2]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[2]^2\right ) K[2]^3-18 J_0(K[2]) J_2(K[2]) Y_0(K[2]) f(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2+18 J_0(K[2]){}^2 Y_2(K[2]) f(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2+9 J_0(K[2]) J_1(K[2]) Y_0(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]-9 J_0(K[2]){}^2 Y_1(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]+9 J_0(K[2]) J_2(K[2]) Y_1(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]-9 J_0(K[2]) J_1(K[2]) Y_2(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]-36 J_0(K[2]) J_1(K[2]) Y_0(K[2]) f(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]+36 J_0(K[2]){}^2 Y_1(K[2]) f(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]+36 J_1(K[2]){}^2 Y_0(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )-9 J_0(K[2]) J_2(K[2]) Y_0(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )-36 J_0(K[2]) J_1(K[2]) Y_1(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )+9 J_0(K[2]){}^2 Y_2(K[2]) f(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )}{4 (J_1(K[2]) Y_0(K[2])-J_0(K[2]) Y_1(K[2])) \left (-16 J_1(K[2]) Y_0(K[2]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[2]^2\right ) K[2]^4+16 J_0(K[2]) Y_1(K[2]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[2]^2\right ) K[2]^4+18 J_2(K[2]) Y_0(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^3-18 J_0(K[2]) Y_2(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^3-9 J_1(K[2]) Y_0(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2+9 J_0(K[2]) Y_1(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2-9 J_2(K[2]) Y_1(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2+9 J_1(K[2]) Y_2(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2-36 J_1(K[2]) Y_0(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2+36 J_0(K[2]) Y_1(K[2]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[2]^2\right ) K[2]^2+9 J_2(K[2]) Y_0(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]-9 J_0(K[2]) Y_2(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right ) K[2]-36 J_1(K[2]) Y_0(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )+36 J_0(K[2]) Y_1(K[2]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[2]^2\right )\right )}-\frac {J_0(K[2]) f(K[2])}{4 (J_0(K[2]) Y_1(K[2])-J_1(K[2]) Y_0(K[2])) K[2]}\right ) \, dK[2]+2 \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {x^2}{4}\right ) \int _1^x \frac {9 (J_1(K[3]) Y_0(K[3])-J_0(K[3]) Y_1(K[3])) f(K[3]) K[3]}{16 J_1(K[3]) Y_0(K[3]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[3]^2\right ) K[3]^4-16 J_0(K[3]) Y_1(K[3]) \, _1F_2\left (3;\frac {5}{2},\frac {5}{2};-\frac {1}{4} K[3]^2\right ) K[3]^4-18 J_2(K[3]) Y_0(K[3]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[3]^2\right ) K[3]^3+18 J_0(K[3]) Y_2(K[3]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[3]^2\right ) K[3]^3+9 J_1(K[3]) Y_0(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right ) K[3]^2-9 J_0(K[3]) Y_1(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right ) K[3]^2+9 J_2(K[3]) Y_1(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right ) K[3]^2-9 J_1(K[3]) Y_2(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right ) K[3]^2+36 J_1(K[3]) Y_0(K[3]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[3]^2\right ) K[3]^2-36 J_0(K[3]) Y_1(K[3]) \, _1F_2\left (2;\frac {3}{2},\frac {3}{2};-\frac {1}{4} K[3]^2\right ) K[3]^2-9 J_2(K[3]) Y_0(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right ) K[3]+9 J_0(K[3]) Y_2(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right ) K[3]+36 J_1(K[3]) Y_0(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right )-36 J_0(K[3]) Y_1(K[3]) \, _1F_2\left (1;\frac {1}{2},\frac {1}{2};-\frac {1}{4} K[3]^2\right )} \, dK[3]}{x}\right \}\right \}\]
✓ Maple : cpu = 0.374 (sec), leaf count = 1851
\[ \left \{ y \left ( x \right ) =-{\frac {1}{x} \left ( \int \!9\,{\frac { \left ( -G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{2}+{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right )-{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ) \right ) f \left ( x \right ) }{-4\,G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{{\sl J}_{1}\left (x\right )}{x}^{5}-9\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{4}+12\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{x}^{4}-8\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{x}^{4}+9\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){x}^{2}-9\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){x}^{2}-81\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{2}+144\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){x}^{2}-36\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ){x}^{2}+36\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x-72\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x+18\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x-27\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right )+63\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right )-18\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right )}}\,{\rm d}x{{\sl J}_{0}\left (x\right )}x+\int \!{\frac {9\,f \left ( x \right ) }{2} \left ( 2\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{2}-{\mbox {$_1$F$_2$}(1;\,{\frac {1}{2}},{\frac {1}{2}};\,-{\frac {{x}^{2}}{4}})}{{\sl J}_{1}\left (x\right )}x+{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,{\frac {1}{2}},{\frac {1}{2}};\,-{\frac {{x}^{2}}{4}})} \right ) \left ( -4\,G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{{\sl J}_{1}\left (x\right )}{x}^{5}-9\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{4}+12\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{x}^{4}-8\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{x}^{4}+9\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){x}^{2}-9\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){x}^{2}-81\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{2}+144\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){x}^{2}-36\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ){x}^{2}+36\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x-72\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x+18\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x-27\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right )+63\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right )-18\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ) \right ) ^{-1}}\,{\rm d}xG^{3, 1}_{1, 3}\left ({\frac {{x}^{2}}{4}}\, \Big \vert \,^{-{\frac {1}{2}}}_{0, 0, -{\frac {1}{2}}}\right )x-\int \!{\frac {9\,xf \left ( x \right ) }{2} \left ( -G^{3, 1}_{1, 3}\left ({\frac {{x}^{2}}{4}}\, \Big \vert \,^{-{\frac {1}{2}}}_{0, 0, -{\frac {1}{2}}}\right ){{\sl J}_{1}\left (x\right )}x+3\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right )-2\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ) \right ) \left ( -4\,G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{{\sl J}_{1}\left (x\right )}{x}^{5}-9\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{4}+12\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{x}^{4}-8\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(3;\,5/2,5/2;\,-1/4\,{x}^{2})}{x}^{4}+9\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){x}^{2}-9\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){x}^{2}-81\,{{\sl J}_{0}\left (x\right )}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}{x}^{2}+144\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){x}^{2}-36\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(2;\,3/2,3/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ){x}^{2}+36\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x-72\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x+18\,{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ){{\sl J}_{1}\left (x\right )}x-27\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-1/2}_{0, 0, -1/2}\right )+63\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-3/2}_{0, 0, -1/2}\right )-18\,{{\sl J}_{0}\left (x\right )}{\mbox {$_1$F$_2$}(1;\,1/2,1/2;\,-1/4\,{x}^{2})}G^{3, 1}_{1, 3}\left (1/4\,{x}^{2}\, \Big \vert \,^{-5/2}_{0, 0, -1/2}\right ) \right ) ^{-1}}\,{\rm d}x{\mbox {$_1$F$_2$}(1;\,{\frac {1}{2}},{\frac {1}{2}};\,-{\frac {{x}^{2}}{4}})} \right ) }+{\it \_C1}\,{{\sl J}_{0}\left (x\right )}+{\frac {{\it \_C2}}{x}{\mbox {$_1$F$_2$}(1;\,{\frac {1}{2}},{\frac {1}{2}};\,-{\frac {{x}^{2}}{4}})}}+{\it \_C3}\,G^{3, 1}_{1, 3}\left ({\frac {{x}^{2}}{4}}\, \Big \vert \,^{-{\frac {1}{2}}}_{0, 0, -{\frac {1}{2}}}\right ) \right \} \]