2.147   ODE No. 147

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

$$a{x}^{2}y(x{)}^3+by(x{)}^2+x^2{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.634131 (sec), leaf count = 343

$$\text{Solve}[\frac{(\frac{b^{2/3}}{2^{2/3}\sqrt[3]{a}x}+\frac{1}{2^{2/3}\sqrt[3]{a}\sqrt[3]{b}y(x)})\text{Ai}({(\frac{b^{2/3}}{2^{2/3}\sqrt[3]{a}x}+\frac{1}{2^{2/3}\sqrt[3]{a}y(x)\sqrt[3]{b}})}^2-\frac{\sqrt[3]{a}x}{\sqrt[3]{2}{b}^{2/3}})+{\text{Ai}}^{\prime }({(\frac{b^{2/3}}{2^{2/3}\sqrt[3]{a}x}+\frac{1}{2^{2/3}\sqrt[3]{a}y(x)\sqrt[3]{b}})}^2-\frac{\sqrt[3]{a}x}{\sqrt[3]{2}{b}^{2/3}})}{(\frac{b^{2/3}}{2^{2/3}\sqrt[3]{a}x}+\frac{1}{2^{2/3}\sqrt[3]{a}\sqrt[3]{b}y(x)})\text{Bi}({(\frac{b^{2/3}}{2^{2/3}\sqrt[3]{a}x}+\frac{1}{2^{2/3}\sqrt[3]{a}y(x)\sqrt[3]{b}})}^2-\frac{\sqrt[3]{a}x}{\sqrt[3]{2}{b}^{2/3}})+{\text{Bi}}^{\prime }({(\frac{b^{2/3}}{2^{2/3}\sqrt[3]{a}x}+\frac{1}{2^{2/3}\sqrt[3]{a}y(x)\sqrt[3]{b}})}^2-\frac{\sqrt[3]{a}x}{\sqrt[3]{2}{b}^{2/3}})}+c_1=0,y(x)]$$ ✓ Maple : cpu = 0.16 (sec), leaf count = 178

$$\{y\left(x\right)=-\sqrt[3]{2}abx{(\sqrt[3]{2}a{b}^2-2{\left(a^2{b}^2\right)}^{2/3}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\mathrm{B}\mathrm{i}(-1/2\frac{a{2}^{2/3}x-2{\mathit{\_}\mathit{Z}}^2\sqrt[3]{a^2{b}^2}}{\sqrt[3]{a^2{b}^2}})\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}+\mathit{\_}\mathit{Z}\mathrm{A}\mathrm{i}(-1/2\frac{a{2}^{2/3}x-2{\mathit{\_}\mathit{Z}}^2\sqrt[3]{a^2{b}^2}}{\sqrt[3]{a^2{b}^2}})+{\mathrm{B}\mathrm{i}}^{(1)}(-1/2\frac{a{2}^{2/3}x-2{\mathit{\_}\mathit{Z}}^2\sqrt[3]{a^2{b}^2}}{\sqrt[3]{a^2{b}^2}})\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{A}\mathrm{i}}^{(1)}(-1/2\frac{a{2}^{2/3}x-2{\mathit{\_}\mathit{Z}}^2\sqrt[3]{a^2{b}^2}}{\sqrt[3]{a^2{b}^2}}))x)}^{-1}\}$$