2.1085   ODE No. 1085

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

$$-y^{\prime }(x)(\frac{(2v-1)g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)}+\frac{2h^{\prime }(x)}{h(x)})+y(x)(g^{\prime }(x{)}^2+\frac{h^{\prime }(x)(\frac{(2v-1)g^{\prime }(x)}{g(x)}+\frac{g^{″}(x)}{g^{\prime }(x)}+\frac{2h^{\prime }(x)}{h(x)})}{h(x)}-\frac{h^{″}(x)}{h(x)})+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.895187 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.08 (sec), leaf count = 29

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_v\left(g\left(x\right)\right)h\left(x\right){\left(g\left(x\right)\right)}^v+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_v\left(g\left(x\right)\right)h\left(x\right){\left(g\left(x\right)\right)}^v\}$$