3.230   ODE No. 230

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

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

Mathematica: cpu = 0.121515 (sec), leaf count = 96 $$\{\{y(x)\to -e^{-\frac{bx}{a}}\sqrt{2{\int }_1^x-\frac{f(K[1])e^{\frac{2bK[1]}{a}}}{a}dK[1]+c_1}\},\{y(x)\to e^{-\frac{bx}{a}}\sqrt{2{\int }_1^x-\frac{f(K[1])e^{\frac{2bK[1]}{a}}}{a}dK[1]+c_1}\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 104 $$\{y\left(x\right)=\frac{1}{a}\sqrt{-{\mathrm{e}}^{2\frac{bx}{a}}a(-\mathit{\_}\mathit{C}\mathit{1}a+2\int {\left({\mathrm{e}}^{\frac{bx}{a}}\right)}^{2}f\left(x\right)\mathrm{d}x)}{\left({\mathrm{e}}^{2\frac{bx}{a}}\right)}^{-1},y\left(x\right)=-\frac{1}{a}\sqrt{-{\mathrm{e}}^{2\frac{bx}{a}}a(-\mathit{\_}\mathit{C}\mathit{1}a+2\int {\left({\mathrm{e}}^{\frac{bx}{a}}\right)}^{2}f\left(x\right)\mathrm{d}x)}{\left({\mathrm{e}}^{2\frac{bx}{a}}\right)}^{-1}\}$$