8.84   ODE No. 1674

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(2a+b-1)x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(c^2{b}^2{x}^{2b}+a(a+b))y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.066008 (sec), leaf count = 106 $$\left\{\{y(x)\to c_2{2}^{-\frac{a+b}{b}}{c}^{\frac{a+b}{b}-1}{\left(x^{2b}\right)}^{\frac{a+b}{2b}-\frac{1}{2}}\sin \left(c\sqrt{x^{2b}}\right)+c_1{2}^{-\frac{a}{b}}{c}^{a/b}{\left(x^{2b}\right)}^{\frac{a}{2b}}\cos \left(c\sqrt{x^{2b}}\right)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 27 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left(x^{b}c\right)x^a+\mathit{\_}\mathit{C}\mathit{2}\cos \left(x^{b}c\right)x^a\}$$