2.1083   ODE No. 1083

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

$$-\frac{f^{\prime }(x)y^{\prime }(x)}{f(x)}+y(x)(-\frac{f^{″}(x)}{2f(x)}+\frac{3f^{\prime }(x{)}^2}{4f(x{)}^2}+\frac{(\frac{1}{4}-v^2)g^{\prime }(x{)}^2}{g(x{)}^2}+g^{\prime }(x{)}^2+\frac{g^3(x)}{2g^{\prime }(x)}-\frac{3g^{″}(x{)}^2}{4g^{\prime }(x{)}^2})+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.833417 (sec), leaf count = 0 , could not solve

DSolve[-((Derivative[1][f][x]*Derivative[1][y][x])/f[x]) + y[x]*((3*Derivative[1][f][x]^2)/(4*f[x]^2) + (g^3)[x]/(2*Derivative[1][g][x]) + Derivative[1][g][x]^2 + ((1/4 - v^2)*Derivative[1][g][x]^2)/g[x]^2 - Derivative[2][f][x]/(2*f[x]) - (3*Derivative[2][g][x]^2)/(4*Derivative[1][g][x]^2)) + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.098 (sec), leaf count = 43

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{\frac{f\left(x\right)g\left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)}}{\mathit{J}}_v\left(g\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{2}\sqrt{\frac{f\left(x\right)g\left(x\right)}{\frac{\mathrm{d}}{\mathrm{d}x}g\left(x\right)}}{\mathit{Y}}_v\left(g\left(x\right)\right)\}$$