3.268   ODE No. 268

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

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

Mathematica: cpu = 1.005128 (sec), leaf count = 140 $$\{\{y(x)\to -e^{{\int }_1^x-\frac{g(K[1])}{f(K[1])}dK[1]}\sqrt{2{\int }_1^x-\frac{h(K[2])\exp (-2{\int }_1^{K[2]}-\frac{g(K[1])}{f(K[1])}dK[1])}{f(K[2])}dK[2]+c_1}\},\{y(x)\to e^{{\int }_1^x-\frac{g(K[1])}{f(K[1])}dK[1]}\sqrt{2{\int }_1^x-\frac{h(K[2])\exp (-2{\int }_1^{K[2]}-\frac{g(K[1])}{f(K[1])}dK[1])}{f(K[2])}dK[2]+c_1}\}\}$$

Maple: cpu = 0.063 (sec), leaf count = 124 $$\{y\left(x\right)=1\sqrt{-{\mathrm{e}}^{2\int \frac{g\left(x\right)}{f\left(x\right)}\mathrm{d}x}(2\int \frac{h\left(x\right)}{f\left(x\right)}{\left({\mathrm{e}}^{\int \frac{g\left(x\right)}{f\left(x\right)}\mathrm{d}x}\right)}^2\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{1})}{\left({\mathrm{e}}^{2\int \frac{g\left(x\right)}{f\left(x\right)}\mathrm{d}x}\right)}^{-1},y\left(x\right)=-1\sqrt{-{\mathrm{e}}^{2\int \frac{g\left(x\right)}{f\left(x\right)}\mathrm{d}x}(2\int \frac{h\left(x\right)}{f\left(x\right)}{\left({\mathrm{e}}^{\int \frac{g\left(x\right)}{f\left(x\right)}\mathrm{d}x}\right)}^2\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{1})}{\left({\mathrm{e}}^{2\int \frac{g\left(x\right)}{f\left(x\right)}\mathrm{d}x}\right)}^{-1}\}$$