3.11   ODE No. 11

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

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

Mathematica: cpu = 0.472560 (sec), leaf count = 62 $$\left\{\{y(x)\to c_1{e}^{{\int }_1^x-f(K[1])dK[1]}+e^{{\int }_1^x-f(K[1])dK[1]}{\int }_1^{x}g(K[2])e^{-{\int }_1^{K[2]}-f(K[1])dK[1]}dK[2]\}\right\}$$

Maple: cpu = 0.0 (sec), leaf count = 24 $$\{y\left(x\right)=(\int g\left(x\right){\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1}){\mathrm{e}}^{\int -f\left(x\right)\mathrm{d}x}\}$$

Sage: cpu = 0.096 (sec), leaf count = 0 $$[(c+\int e^{(\int f\left(x\right)dx)}g\left(x\right)dx)e^{(-\int f\left(x\right)dx)},\mathtt{\text{linear}}]$$