4.180   ODE No. 1180

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+3x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(-v^2+x^2+1)y\left(x\right)-f\left(x\right)=0}}$$

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

Mathematica: cpu = 0.231029 (sec), leaf count = 73 $$\left\{\{y(x)\to \frac{J_v(x){\int }_1^x-\frac{1}{2}\pi f(K[1])Y_v(K[1])dK[1]+Y_v(x){\int }_1^x\frac{1}{2}\pi f(K[2])J_v(K[2])dK[2]}{x}+\frac{c_1{J}_v(x)}{x}+\frac{c_2{Y}_v(x)}{x}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 53 $$\{y\left(x\right)=\frac{{\mathit{J}}_v\left(x\right)\mathit{\_}\mathit{C}\mathit{2}}{x}+\frac{{\mathit{Y}}_v\left(x\right)\mathit{\_}\mathit{C}\mathit{1}}{x}+\frac{\pi ({\mathit{Y}}_v\left(x\right)\int {\mathit{J}}_v\left(x\right)f\left(x\right)\mathrm{d}x-{\mathit{J}}_v\left(x\right)\int {\mathit{Y}}_v\left(x\right)f\left(x\right)\mathrm{d}x)}{2x}\}$$