4.395   ODE No. 1395

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

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

Mathematica: cpu = 0.160520 (sec), leaf count = 78 $$\left\{\{y(x)\to c_1{e}^{\frac{\sqrt{-\frac{1}{a^4}}a}{ax+b}}(ax+b)+\frac{c_2{e}^{-\frac{\sqrt{-\frac{1}{a^4}}a}{ax+b}}(ax+b)}{2\sqrt{-\frac{1}{a^4}}{a}^2}\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 43 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}(ax+b)\sin \left(\frac{1}{a(ax+b)}\right)+\mathit{\_}\mathit{C}\mathit{2}(ax+b)\cos \left(\frac{1}{a(ax+b)}\right)\}$$