2.1036   ODE No. 1036

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

$$a{y}^{\prime }(x)+by(x)-f(x)+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.456709 (sec), leaf count = 207

$$\left\{\{y(x)\to e^{\frac{1}{2}x(\sqrt{a^2-4b}-a)}{\int }_1^x\frac{f(K[2])\exp (\frac{1}{2}(-\sqrt{a^2-4b}-a)K[2]+aK[2])}{\sqrt{a^2-4b}}dK[2]+e^{\frac{1}{2}x(-\sqrt{a^2-4b}-a)}{\int }_1^x-\frac{f(K[1])e^{\frac{1}{2}(\sqrt{a^2-4b}-a)K[1]+aK[1]}}{\sqrt{a^2-4b}}dK[1]+c_1{e}^{\frac{1}{2}x(-\sqrt{a^2-4b}-a)}+c_2{e}^{\frac{1}{2}x(\sqrt{a^2-4b}-a)}\}\right\}$$

✓ Maple : cpu = 0.097 (sec), leaf count = 128

$$\{y\left(x\right)={\mathrm{e}}^{(-\frac{a}{2}+\frac{1}{2}\sqrt{a^2-4b})x}\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{(-\frac{a}{2}-\frac{1}{2}\sqrt{a^2-4b})x}\mathit{\_}\mathit{C}\mathit{1}+1(\int f\left(x\right){\mathrm{e}}^{-\frac{x}{2}(-a+\sqrt{a^2-4b})}\mathrm{d}x{\mathrm{e}}^{x\sqrt{a^2-4b}}-\int f\left(x\right){\mathrm{e}}^{\frac{x}{2}(a+\sqrt{a^2-4b})}\mathrm{d}x){\mathrm{e}}^{-\frac{x}{2}(a+\sqrt{a^2-4b})}\frac{1}{\sqrt{a^2-4b}}\}$$