2.1515   ODE No. 1515

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

$$y(x)(a(4c^2{\nu }^2-a^2)+4b^2{c}^2(c-a)x^{2c})+y^{\prime }(x)(3(a-1)ax+4b^2{c}^2{x}^{2c+1}-4c^2{\nu }^2+1)+3(1-a)x^2{y}^{″}(x)+x^3{y}^{(3)}(x)=0$$ ✗ Mathematica : cpu = 0.150694 (sec), leaf count = 0 , could not solve

DSolve[(a*(-a^2 + 4*c^2*nu^2) + 4*b^2*c^2*(-a + c)*x^(2*c))*y[x] + (1 - 4*c^2*nu^2 + 3*(-1 + a)*a*x + 4*b^2*c^2*x^(1 + 2*c))*Derivative[1][y][x] + 3*(1 - a)*x^2*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0, y[x], x]

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

$$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}\mathit{\_}\mathit{Y}\left(x\right)+(-3a{x}^2+3x^2)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+(4b^2{c}^2{x}^{2c+1}-4{\nu }^2{c}^2+3a^{2}x-3ax+1)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(-4x^{2c}a{b}^2{c}^2+4x^{2c}{b}^2{c}^3+4a{c}^2{\nu }^2-a^3)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$