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 = 0.0073409 (sec), leaf count = 115

$$\left\{\{x(t)\to c_2\exp ({\int }_1^{t}f(K[2])dK[2])\sin ({\int }_1^{t}g(K[1])dK[1])+c_1\exp ({\int }_1^{t}f(K[2])dK[2])\cos ({\int }_1^{t}g(K[1])dK[1]),y(t)\to c_2\exp ({\int }_1^{t}f(K[2])dK[2])\cos ({\int }_1^{t}g(K[1])dK[1])-c_1\exp ({\int }_1^{t}f(K[2])dK[2])\sin ({\int }_1^{t}g(K[1])dK[1])\}\right\}$$ ✓ Maple : cpu = 0.317 (sec), leaf count = 57

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