10.19   ODE No. 1874

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

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

Mathematica: cpu = 0.062508 (sec), leaf count = 107 $$\left\{\{x(t)\to c_2{e}^{{\int }_1^{t}f(K[2])dK[2]}\sin ({\int }_1^{t}g(K[1])dK[1])+c_1{e}^{{\int }_1^{t}f(K[2])dK[2]}\cos ({\int }_1^{t}g(K[1])dK[1]),y(t)\to c_2{e}^{{\int }_1^{t}f(K[2])dK[2]}\cos ({\int }_1^{t}g(K[1])dK[1])-c_1{e}^{{\int }_1^{t}f(K[2])dK[2]}\sin ({\int }_1^{t}g(K[1])dK[1])\}\right\}$$

Maple: cpu = 0.296 (sec), leaf count = 57 $$\left\{\{x\left(t\right)={\mathrm{e}}^{\int \tan (\mathit{\_}\mathit{C}\mathit{1}-\int g\left(t\right)\mathrm{d}t)g\left(t\right)+f\left(t\right)\mathrm{d}t}\mathit{\_}\mathit{C}\mathit{2},y\left(t\right)=\tan (\mathit{\_}\mathit{C}\mathit{1}-\int g\left(t\right)\mathrm{d}t){\mathrm{e}}^{\int \tan (\mathit{\_}\mathit{C}\mathit{1}-\int g\left(t\right)\mathrm{d}t)g\left(t\right)+f\left(t\right)\mathrm{d}t}\mathit{\_}\mathit{C}\mathit{2}\}\right\}$$