2.1874   ODE No. 1874

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

$$\{x^{\prime }(t)=f(t)x(t)+g(t)y(t),y^{\prime }(t)=f(t)y(t)-g(t)x(t)\}$$ ✓ Mathematica : cpu = 0.138726 (sec), leaf count = 131

$$\left\{\{x(t)\to c_2{e}^{\text{Integrate}[f(K[2]),\{K[2],1,t\},\text{Assumptions}\to \text{True}]}\sin (\text{Integrate}[g(K[1]),\{K[1],1,t\},\text{Assumptions}\to \text{True}])+c_1{e}^{\text{Integrate}[f(K[2]),\{K[2],1,t\},\text{Assumptions}\to \text{True}]}\cos (\text{Integrate}[g(K[1]),\{K[1],1,t\},\text{Assumptions}\to \text{True}]),y(t)\to c_2{e}^{\text{Integrate}[f(K[2]),\{K[2],1,t\},\text{Assumptions}\to \text{True}]}\cos (\text{Integrate}[g(K[1]),\{K[1],1,t\},\text{Assumptions}\to \text{True}])-c_1{e}^{\text{Integrate}[f(K[2]),\{K[2],1,t\},\text{Assumptions}\to \text{True}]}\sin (\text{Integrate}[g(K[1]),\{K[1],1,t\},\text{Assumptions}\to \text{True}])\}\right\}$$

✓ Maple : cpu = 0.407 (sec), leaf count = 57

$$\left\{\{x\left(t\right)={\mathrm{e}}^{\int \tan (\mathit{\_}\mathit{C}\mathit{1}-\int g\left(t\right)\mathrm{d}t)g\left(t\right)+f\left(t\right)\mathrm{d}t}\mathit{\_}\mathit{C}\mathit{2},y\left(t\right)=\tan (\mathit{\_}\mathit{C}\mathit{1}-\int g\left(t\right)\mathrm{d}t){\mathrm{e}}^{\int \tan (\mathit{\_}\mathit{C}\mathit{1}-\int g\left(t\right)\mathrm{d}t)g\left(t\right)+f\left(t\right)\mathrm{d}t}\mathit{\_}\mathit{C}\mathit{2}\}\right\}$$