2.1912   ODE No. 1912

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

$$\{{\text{x1}}^{\prime }(t)=a\text{x2}(t)+b\text{x3}(t)\cos (ct)+b\text{x4}(t)\sin (ct),{\text{x2}}^{\prime }(t)=-a\text{x1}(t)+b\text{x3}(t)\sin (ct)-b\text{x4}(t)\cos (ct),{\text{x3}}^{\prime }(t)=a\text{x4}(t)-b\text{x1}(t)\cos (ct)-b\text{x2}(t)\sin (ct),{\text{x4}}^{\prime }(t)=-a\text{x3}(t)-b\text{x1}(t)\sin (ct)+b\text{x2}(t)\cos (ct)\}$$ ✗ Mathematica : cpu = 0.0638185 (sec), leaf count = 0 , could not solve

DSolve[{Derivative[1][x1][t] == a*x2[t] + b*Cos[c*t]*x3[t] + b*Sin[c*t]*x4[t], Derivative[1][x2][t] == -(a*x1[t]) + b*Sin[c*t]*x3[t] - b*Cos[c*t]*x4[t], Derivative[1][x3][t] == -(b*Cos[c*t]*x1[t]) - b*Sin[c*t]*x2[t] + a*x4[t], Derivative[1][x4][t] == -(b*Sin[c*t]*x1[t]) + b*Cos[c*t]*x2[t] - a*x3[t]}, {x[t], y[t], z[t]}, t]

✓ Maple : cpu = 2.798 (sec), leaf count = 2956

$$\{\{\mathit{x}\mathit{1}\left(t\right)=\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{3}\sin \left(ct\right)+\mathit{\_}\mathit{C}\mathit{4}\cos \left(ct\right),\mathit{x}\mathit{2}\left(t\right)=-\cos \left(ct\right)\mathit{\_}\mathit{C}\mathit{3}+\sin \left(ct\right)\mathit{\_}\mathit{C}\mathit{4}+\mathit{\_}\mathit{C}\mathit{1},\mathit{x}\mathit{3}\left(t\right)=\frac{b(\cos \left(ct\right)\mathit{\_}\mathit{C}\mathit{1}a-\sin \left(ct\right)\mathit{\_}\mathit{C}\mathit{2}a-\mathit{\_}\mathit{C}\mathit{3}(a+c))}{a(a+c)},\mathit{x}\mathit{4}\left(t\right)=\frac{b(\cos \left(ct\right)\mathit{\_}\mathit{C}\mathit{2}a+\sin \left(ct\right)\mathit{\_}\mathit{C}\mathit{1}a+\mathit{\_}\mathit{C}\mathit{4}(a+c))}{a(a+c)}\},\{\mathit{x}\mathit{1}\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{t}{2}\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{c^2(4a^2+4ca+4b^2+c^2)}}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{t}{2}\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{c^2(4a^2+4ca+4b^2+c^2)}}}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-\frac{t}{2}\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{c^2(4a^2+4ca+4b^2+c^2)}}}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{\frac{t}{2}\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{c^2(4a^2+4ca+4b^2+c^2)}}},\mathit{x}\mathit{2}\left(t\right)=\frac{1}{8c(a^2+ca+b^2)}(-4\mathit{\_}\mathit{C}\mathit{1}(1/4{(-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}+\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}(a^2+ca+b^2+c^2)){\mathrm{e}}^{-1/2\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}+4\mathit{\_}\mathit{C}\mathit{2}(1/4{(-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}+\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}(a^2+ca+b^2+c^2)){\mathrm{e}}^{1/2\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}-4(\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-1/2\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}-\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{1/2\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t})(1/4{(-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}+(a^2+ca+b^2+c^2)\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}})),\mathit{x}\mathit{3}\left(t\right)=\frac{1}{8bc(a^2+ca+b^2)}(8\mathit{\_}\mathit{C}\mathit{1}(1/8a{(-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}\cos \left(ct\right)+1/2\cos \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}+(1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))\sin \left(ct\right)(a^2+ca+b^2)){\mathrm{e}}^{-1/2\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}+8(-1/8a{(-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}\cos \left(ct\right)-1/2\cos \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}+(1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))\sin \left(ct\right)(a^2+ca+b^2))\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{1/2\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}+8\mathit{\_}\mathit{C}\mathit{3}(1/8a{(-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}\cos \left(ct\right)+1/2\cos \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}+\sin \left(ct\right)(-1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))(a^2+ca+b^2)){\mathrm{e}}^{-1/2\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}+8(-1/8a{(-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}\cos \left(ct\right)-1/2\cos \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}+\sin \left(ct\right)(-1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))(a^2+ca+b^2))\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{1/2\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}),\mathit{x}\mathit{4}\left(t\right)=\frac{1}{8bc(a^2+ca+b^2)}(4\mathit{\_}\mathit{C}\mathit{1}(1/4a\sin \left(ct\right){(-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}+\sin \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}-2(1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))\cos \left(ct\right)(a^2+ca+b^2)){\mathrm{e}}^{-1/2\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}-4(1/4a\sin \left(ct\right){(-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}+\sin \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}+2(1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))\cos \left(ct\right)(a^2+ca+b^2))\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{1/2\sqrt{-4a^2-4ca-4b^2-2c^2-2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}+4(1/4a{(-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}\sin \left(ct\right)+\sin \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}-2\cos \left(ct\right)(-1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))(a^2+ca+b^2))\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-1/2\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}-4\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{1/2\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}t}(1/4a{(-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4})}^{3/2}\sin \left(ct\right)+\sin \left(ct\right)(a^3+a{b}^2-b^{2}c)\sqrt{-4a^2-4ca-4b^2-2c^2+2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}}+2\cos \left(ct\right)(-1/2\sqrt{4a^2{c}^2+4c^{3}a+4b^2{c}^2+c^4}+c(a+c/2))(a^2+ca+b^2)))\}\}$$