2.1465   ODE No. 1465

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

$$-a^2{y}^{\prime }(x)+2a^{2}y(x)+y^{(3)}(x)-2y^{″}(x)-\sinh (x)=0$$ ✓ Mathematica : cpu = 0.086237 (sec), leaf count = 95

$$\left\{\{y(x)\to \frac{e^{-x}(3a^2{e}^{2x}-a^2-3e^{2x}-12e^x\sinh (x)-6e^x\cosh (x)+1)}{6(a-2)(a+2)(a^2-1)}+c_1{e}^{-ax}+c_3{e}^{ax}+c_2{e}^{2x}\}\right\}$$

✓ Maple : cpu = 0.089 (sec), leaf count = 467

$$\{y\left(x\right)=-\frac{-2{\mathrm{e}}^{2x}\cosh \left(3x\right)a-9{\mathrm{e}}^{ax}\sinh \left((a-1)x\right)a-3{\mathrm{e}}^{ax}\cosh \left((a+1)x\right)a+9{\mathrm{e}}^{ax}\cosh \left((a-1)x\right)a+3{\mathrm{e}}^{ax}\sinh \left((a+1)x\right)a-3{\mathrm{e}}^{-ax}\sinh \left((a-1)x\right)a+9{\mathrm{e}}^{-ax}\cosh \left((a+1)x\right)a-3{\mathrm{e}}^{-ax}\cosh \left((a-1)x\right)a+9{\mathrm{e}}^{-ax}\sinh \left((a+1)x\right)a+2{\mathrm{e}}^{2x}\sinh \left(3x\right)a+6\sinh \left(x\right){\mathrm{e}}^{2x}{a}^3+3{\mathrm{e}}^{-ax}\cosh \left((a-1)x\right)a^2-3{\mathrm{e}}^{-ax}\sinh \left((a+1)x\right)a^2-6\sinh \left(x\right){\mathrm{e}}^{2x}a+6{\mathrm{e}}^{2x}\cosh \left(x\right)a-3{\mathrm{e}}^{-ax}\cosh \left((a+1)x\right)a^2+3{\mathrm{e}}^{ax}\cosh \left((a-1)x\right)a^2+3{\mathrm{e}}^{ax}\sinh \left((a+1)x\right)a^2+3{\mathrm{e}}^{-ax}\sinh \left((a-1)x\right)a^2+2{\mathrm{e}}^{2x}\cosh \left(3x\right)a^3-3{\mathrm{e}}^{ax}\sinh \left((a-1)x\right)a^2-3{\mathrm{e}}^{ax}\cosh \left((a+1)x\right)a^2-6{\mathrm{e}}^{2x}\cosh \left(x\right)a^3-2{\mathrm{e}}^{2x}\sinh \left(3x\right)a^3-6{\mathrm{e}}^{ax}\sinh \left((a-1)x\right)+6{\mathrm{e}}^{ax}\cosh \left((a+1)x\right)+6{\mathrm{e}}^{ax}\cosh \left((a-1)x\right)-6{\mathrm{e}}^{ax}\sinh \left((a+1)x\right)-6{\mathrm{e}}^{-ax}\sinh \left((a-1)x\right)-6{\mathrm{e}}^{-ax}\cosh \left((a+1)x\right)-6{\mathrm{e}}^{-ax}\cosh \left((a-1)x\right)-6{\mathrm{e}}^{-ax}\sinh \left((a+1)x\right)}{12a(a^2-4)(a-1)(a+1)}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{ax}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-ax}\}$$