2.1440   ODE No. 1440

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

$$y^{″}(x)=-\frac{y^{\prime }(x)(-{\varphi }^{″}(x)-\varphi (x){\varphi }^{\prime }(x)+\varphi \left(x^3\right))}{{\varphi }^{\prime }(x)+\varphi (x{)}^2}-\frac{y(x)(-\varphi (x){\varphi }^{″}(x)+\varphi (x{)}^2(-{\varphi }^{\prime }(x))+{\varphi }^{\prime }(x{)}^2)}{{\varphi }^{\prime }(x)+\varphi (x{)}^2}$$ ✗ Mathematica : cpu = 0.871801 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == -((Derivative[1][y][x]*(phi[x^3] - phi[x]*Derivative[1][phi][x] - Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x])) - (y[x]*(-(phi[x]^2*Derivative[1][phi][x]) + Derivative[1][phi][x]^2 - phi[x]*Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x]), y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

$$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{({\left(\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)\right)}^2-{\left(\varphi \left(x\right)\right)}^2\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)-\varphi \left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\varphi \left(x\right))\mathit{\_}\mathit{Y}\left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)+{\left(\varphi \left(x\right)\right)}^2}+\frac{(\varphi \left(x^3\right)-\varphi \left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)-\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\varphi \left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}\varphi \left(x\right)+{\left(\varphi \left(x\right)\right)}^2}+\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$