4.204   ODE No. 1204

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a+2b)x^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+((a+b)b{x}^2-2)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.019002 (sec), leaf count = 132 $$\left\{\{y(x)\to \frac{2c_2{e}^{\frac{1}{2}(-ax-2bx+\log (x))}(i\sinh \left(\frac{ax}{2}\right)-\frac{2i\cosh \left(\frac{ax}{2}\right)}{ax})}{\sqrt{\pi }\sqrt{-iax}}+\frac{2c_1{e}^{\frac{1}{2}(-ax-2bx+\log (x))}(\frac{2\sinh \left(\frac{ax}{2}\right)}{ax}-\cosh \left(\frac{ax}{2}\right))}{\sqrt{\pi }\sqrt{-iax}}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 37 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-bx}(ax-2)}{x}+\frac{\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-(a+b)x}(ax+2)}{x}\}$$