2.43   ODE No. 43

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

$$y(x{)}^3(4a^{2}x+3a{x}^2+b)+y^{\prime }(x)+3xy(x{)}^2=0$$ ✓ Mathematica : cpu = 10.3341 (sec), leaf count = 352

$$\text{Solve}[c_1=\frac{(3x-a(\sqrt{4-\frac{3b}{a^3}}-2))J_{\frac{1}{2}\sqrt{4-\frac{3b}{a^3}}}(-\frac{1}{2}i\sqrt{\frac{3(b+ax(4a+3x))y(x)-6a}{a^{3}y(x)}})-ia\sqrt{\frac{3y(x)(ax(4a+3x)+b)-6a}{a^{3}y(x)}}{J}_{\frac{1}{2}(\sqrt{4-\frac{3b}{a^3}}+2)}(-\frac{1}{2}i\sqrt{\frac{3(b+ax(4a+3x))y(x)-6a}{a^{3}y(x)}})}{(a(\sqrt{4-\frac{3b}{a^3}}-2)-3x)Y_{\frac{1}{2}\sqrt{4-\frac{3b}{a^3}}}(-\frac{1}{2}i\sqrt{\frac{3(b+ax(4a+3x))y(x)-6a}{a^{3}y(x)}})+ia\sqrt{\frac{3y(x)(ax(4a+3x)+b)-6a}{a^{3}y(x)}}{Y}_{\frac{1}{2}(\sqrt{4-\frac{3b}{a^3}}+2)}(-\frac{1}{2}i\sqrt{\frac{3(b+ax(4a+3x))y(x)-6a}{a^{3}y(x)}})},y(x)]$$

✓ Maple : cpu = 2.198 (sec), leaf count = 373

$$\{\mathit{\_}\mathit{C}\mathit{1}+1(-{\mathit{K}}_{\frac{1}{2}\sqrt{\frac{4a^3-3b}{a^3}}+1}(-\frac{\sqrt{3}}{2}\sqrt{\frac{4y\left(x\right)a^{2}x+3a{x}^{2}y\left(x\right)+by\left(x\right)-2a}{a^{3}y\left(x\right)}})\sqrt{3}\sqrt{\frac{4y\left(x\right)a^{2}x+3a{x}^{2}y\left(x\right)+by\left(x\right)-2a}{a^{3}y\left(x\right)}}a-(a\sqrt{\frac{4a^3-3b}{a^3}}-2a-3x){\mathit{K}}_{\frac{1}{2}\sqrt{\frac{4a^3-3b}{a^3}}}(-\frac{\sqrt{3}}{2}\sqrt{\frac{4y\left(x\right)a^{2}x+3a{x}^{2}y\left(x\right)+by\left(x\right)-2a}{a^{3}y\left(x\right)}})){({\mathit{I}}_{\frac{1}{2}\sqrt{\frac{4a^3-3b}{a^3}}+1}(-\frac{\sqrt{3}}{2}\sqrt{\frac{4y\left(x\right)a^{2}x+3a{x}^{2}y\left(x\right)+by\left(x\right)-2a}{a^{3}y\left(x\right)}})\sqrt{3}\sqrt{\frac{4y\left(x\right)a^{2}x+3a{x}^{2}y\left(x\right)+by\left(x\right)-2a}{a^{3}y\left(x\right)}}a-(a\sqrt{\frac{4a^3-3b}{a^3}}-2a-3x){\mathit{I}}_{\frac{1}{2}\sqrt{\frac{4a^3-3b}{a^3}}}(-\frac{\sqrt{3}}{2}\sqrt{\frac{4y\left(x\right)a^{2}x+3a{x}^{2}y\left(x\right)+by\left(x\right)-2a}{a^{3}y\left(x\right)}}))}^{-1}=0\}$$