5.45   ODE No. 1493

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+4x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(x^2+2)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+3xy\left(x\right)-f\left(x\right)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 7.185412 (sec), leaf count = 2582 $$\left\{\{y(x)\to J_0(x)c_1+2Y_0(x)c_2+\frac{2c_3{}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{x^2}{4})}{x}+\frac{x{J}_0(x){\int }_1^x(\frac{-16J_1(K[1])Y_0(K[1]){}^{2}f(K[1]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^3+16J_0(K[1])Y_0(K[1])Y_1(K[1])f(K[1]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^3+18J_2(K[1])Y_0(K[1]){}^{2}f(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2-18J_0(K[1])Y_0(K[1])Y_2(K[1])f(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2-9J_1(K[1])Y_0(K[1]){}^{2}f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1]+9J_0(K[1])Y_0(K[1])Y_1(K[1])f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1]-9J_2(K[1])Y_0(K[1])Y_1(K[1])f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1]+9J_1(K[1])Y_0(K[1])Y_2(K[1])f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1]+36J_1(K[1])Y_0(K[1]){}^{2}f(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1]-36J_0(K[1])Y_0(K[1])Y_1(K[1])f(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1]+9J_2(K[1])Y_0(K[1]){}^{2}f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)+36J_0(K[1])Y_1(K[1]){}^{2}f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)-36J_1(K[1])Y_0(K[1])Y_1(K[1])f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)-9J_0(K[1])Y_0(K[1])Y_2(K[1])f(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)}{2(J_0(K[1])Y_1(K[1])-J_1(K[1])Y_0(K[1]))(16J_1(K[1])Y_0(K[1]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^4-16J_0(K[1])Y_1(K[1]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^4-18J_2(K[1])Y_0(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^3+18J_0(K[1])Y_2(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^3+9J_1(K[1])Y_0(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2-9J_0(K[1])Y_1(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2+9J_2(K[1])Y_1(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2-9J_1(K[1])Y_2(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2+36J_1(K[1])Y_0(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2-36J_0(K[1])Y_1(K[1]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[1{]}^2)K[1{]}^2-9J_2(K[1])Y_0(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1]+9J_0(K[1])Y_2(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)K[1]+36J_1(K[1])Y_0(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2)-36J_0(K[1])Y_1(K[1]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[1{]}^2))}-\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]})dK[1]+2x{Y}_0(x){\int }_1^x(\frac{16J_0(K[2])J_1(K[2])Y_0(K[2])f(K[2]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^3-16J_0(K[2]){}^2{Y}_1(K[2])f(K[2]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^3-18J_0(K[2])J_2(K[2])Y_0(K[2])f(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2+18J_0(K[2]){}^2{Y}_2(K[2])f(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2+9J_0(K[2])J_1(K[2])Y_0(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2]-9J_0(K[2]){}^2{Y}_1(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2]+9J_0(K[2])J_2(K[2])Y_1(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2]-9J_0(K[2])J_1(K[2])Y_2(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2]-36J_0(K[2])J_1(K[2])Y_0(K[2])f(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2]+36J_0(K[2]){}^2{Y}_1(K[2])f(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2]+36J_1(K[2]){}^2{Y}_0(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)-9J_0(K[2])J_2(K[2])Y_0(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)-36J_0(K[2])J_1(K[2])Y_1(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)+9J_0(K[2]){}^2{Y}_2(K[2])f(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)}{4(J_1(K[2])Y_0(K[2])-J_0(K[2])Y_1(K[2]))(-16J_1(K[2])Y_0(K[2]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^4+16J_0(K[2])Y_1(K[2]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^4+18J_2(K[2])Y_0(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^3-18J_0(K[2])Y_2(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^3-9J_1(K[2])Y_0(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2+9J_0(K[2])Y_1(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2-9J_2(K[2])Y_1(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2+9J_1(K[2])Y_2(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2-36J_1(K[2])Y_0(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2+36J_0(K[2])Y_1(K[2]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[2{]}^2)K[2{]}^2+9J_2(K[2])Y_0(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2]-9J_0(K[2])Y_2(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)K[2]-36J_1(K[2])Y_0(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2)+36J_0(K[2])Y_1(K[2]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[2{]}^2))}-\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]})dK[2]+2{}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{x^2}{4}){\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]}{16J_1(K[3])Y_0(K[3]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^4-16J_0(K[3])Y_1(K[3]){}_1{F}_2(3;\frac{5}{2},\frac{5}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^4-18J_2(K[3])Y_0(K[3]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^3+18J_0(K[3])Y_2(K[3]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^3+9J_1(K[3])Y_0(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^2-9J_0(K[3])Y_1(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^2+9J_2(K[3])Y_1(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^2-9J_1(K[3])Y_2(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^2+36J_1(K[3])Y_0(K[3]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^2-36J_0(K[3])Y_1(K[3]){}_1{F}_2(2;\frac{3}{2},\frac{3}{2};-\frac{1}{4}K[3{]}^2)K[3{]}^2-9J_2(K[3])Y_0(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)K[3]+9J_0(K[3])Y_2(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)K[3]+36J_1(K[3])Y_0(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)-36J_0(K[3])Y_1(K[3]){}_1{F}_2(1;\frac{1}{2},\frac{1}{2};-\frac{1}{4}K[3{]}^2)}dK[3]}{x}\}\right\}$$

Maple: cpu = 0.265 (sec), leaf count = 1849 $$\{y\left(x\right)=\frac{1}{x}(\int 9\frac{({}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2+G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-{}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right))f\left(x\right)}{-4{}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_1\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^5-9{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^4-8G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_0\left(x\right)x^4+12{}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^4+144{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right)x^2-36{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_0\left(x\right)x^2-81{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2-9G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x^2+9{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2-72G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x+18G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x+36{\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x+63G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-18G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-27{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)}\mathrm{d}x{\mathit{J}}_0\left(x\right)x-\int \frac{9f\left(x\right)}{2}(2{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)x^2-{\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;\frac{1}{2},\frac{1}{2};-\frac{x^2}{4})x+{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;\frac{1}{2},\frac{1}{2};-\frac{x^2}{4})){(-4{}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_1\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^5-9{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^4-8G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_0\left(x\right)x^4+12{}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^4+144{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right)x^2-36{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_0\left(x\right)x^2-81{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2-9G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x^2+9{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2-72G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x+18G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x+36{\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x+63G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-18G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-27{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right))}^{-1}\mathrm{d}x{G}_{1,3}^{3,1}\left(\frac{x^2}{4}|{}_{0,0,-\frac{1}{2}}^{-\frac{1}{2}}\right)x-\int \frac{9xf\left(x\right)}{2}({\mathit{J}}_1\left(x\right)G_{1,3}^{3,1}\left(\frac{x^2}{4}|{}_{0,0,-\frac{1}{2}}^{-\frac{1}{2}}\right)x+2{\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right)-3{\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)){(-4{}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_1\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^5-9{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^4-8G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_0\left(x\right)x^4+12{}_1\text{F}{}_2(3;5/2,5/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^4+144{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right)x^2-36{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_0\left(x\right)x^2-81{}_1\text{F}{}_2(2;3/2,3/2;-1/4x^2){\mathit{J}}_0\left(x\right)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2-9G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x^2+9{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x^2-72G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x+18G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)x+36{\mathit{J}}_1\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right)x+63G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-3/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-18G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-5/2}\right){\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)-27{\mathit{J}}_0\left(x\right){}_1\text{F}{}_2(1;1/2,1/2;-1/4x^2)G_{1,3}^{3,1}\left(1/4x^2|{}_{0,0,-1/2}^{-1/2}\right))}^{-1}\mathrm{d}x{}_1\text{F}{}_2(1;\frac{1}{2},\frac{1}{2};-\frac{x^2}{4}))+\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_0\left(x\right)+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x}{}_1\text{F}{}_2(1;\frac{1}{2},\frac{1}{2};-\frac{x^2}{4})+\mathit{\_}\mathit{C}\mathit{3}{G}_{1,3}^{3,1}\left(\frac{x^2}{4}|{}_{0,0,-\frac{1}{2}}^{-\frac{1}{2}}\right)\}$$