3.49   ODE No. 49

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+a\left(\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)\right){\left(y\left(x\right)\right)}^3+6a\varphi \left(x\right){\left(y\left(x\right)\right)}^2+\frac{(2a+1)y\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\varphi \left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)}+2a+2=0}}$$

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

Mathematica: cpu = 28.631636 (sec), leaf count = 52 $$\text{DSolve}[ay(x{)}^3{\varphi }^{\prime }(x)+\frac{(2a+1)y(x){\varphi }^{″}(x)}{{\varphi }^{\prime }(x)}+6a\varphi (x)y(x{)}^2+2a+y^{\prime }(x)+2=0,y(x),x]$$

Maple: cpu = 0.702 (sec), leaf count = 0 $$\text{could not solve}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$