2.426   ODE No. 426

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

$$(3x+1)y^{\prime }(x{)}^2-3(y(x)+2)y^{\prime }(x)+9=0$$ ✓ Mathematica : cpu = 0.389446 (sec), leaf count = 310

$$\{\{y(x)\to -\frac{\sqrt{9x^2\sinh \left(c_1\right)+9x^2\cosh \left(c_1\right)-210x\sinh \left(c_1\right)+6x\sinh \left(2c_1\right)-210x\cosh \left(c_1\right)+6x\cosh \left(2c_1\right)+1225\sinh \left(c_1\right)-70\sinh \left(2c_1\right)+\sinh \left(3c_1\right)+1225\cosh \left(c_1\right)-70\cosh \left(2c_1\right)+\cosh \left(3c_1\right)}}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}+\frac{18x}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}-\frac{8\cosh \left(c_1\right)}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}-\frac{8\sinh \left(c_1\right)}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}+\frac{294}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}\},\{y(x)\to \frac{\sqrt{9x^2\sinh \left(c_1\right)+9x^2\cosh \left(c_1\right)-210x\sinh \left(c_1\right)+6x\sinh \left(2c_1\right)-210x\cosh \left(c_1\right)+6x\cosh \left(2c_1\right)+1225\sinh \left(c_1\right)-70\sinh \left(2c_1\right)+\sinh \left(3c_1\right)+1225\cosh \left(c_1\right)-70\cosh \left(2c_1\right)+\cosh \left(3c_1\right)}}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}+\frac{18x}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}-\frac{8\cosh \left(c_1\right)}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}-\frac{8\sinh \left(c_1\right)}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}+\frac{294}{\sinh \left(c_1\right)+\cosh \left(c_1\right)-36}\}\}$$

✓ Maple : cpu = 0.043 (sec), leaf count = 49

$$\{y\left(x\right)=-2-2\sqrt{3x+1},y\left(x\right)=-2+2\sqrt{3x+1},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2-6\mathit{\_}\mathit{C}\mathit{1}+9}{3\mathit{\_}\mathit{C}\mathit{1}}\}$$