2.1531   ODE No. 1531

\[ A(x) \left (f(x) y''(x)+g(x) y'(x)+h(x) y(x)\right )+f'(x) y''(x)+f(x) y^{(3)}(x)+g'(x) y'(x)+g(x) y''(x)+y(x) h'(x)+h(x) y'(x)=0 \]

✗ Mathematica : cpu = 0.0285001 (sec), leaf count = 0

DSolve[y[x]*Derivative[1][h][x] + h[x]*Derivative[1][y][x] + Derivative[1][g][x]*Derivative[1][y][x] + g[x]*Derivative[2][y][x] + Derivative[1][f][x]*Derivative[2][y][x] + A[x]*(h[x]*y[x] + g[x]*Derivative[1][y][x] + f[x]*Derivative[2][y][x]) + f[x]*Derivative[3][y][x] == 0,y[x],x]
 

, could not solve

DSolve[y[x]*Derivative[1][h][x] + h[x]*Derivative[1][y][x] + Derivative[1][g][x]*Derivative[1][y][x] + g[x]*Derivative[2][y][x] + Derivative[1][f][x]*Derivative[2][y][x] + A[x]*(h[x]*y[x] + g[x]*Derivative[1][y][x] + f[x]*Derivative[2][y][x]) + f[x]*Derivative[3][y][x] == 0, y[x], x]

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

dsolve(diff(f(x),x)*diff(diff(y(x),x),x)+f(x)*diff(diff(diff(y(x),x),x),x)+diff(g(x),x)*diff(y(x),x)+g(x)*diff(diff(y(x),x),x)+diff(h(x),x)*y(x)+h(x)*diff(y(x),x)+A(x)*(f(x)*diff(diff(y(x),x),x)+g(x)*diff(y(x),x)+h(x)*y(x))=0,y(x))
 

, result contains DESol or ODESolStruc

\[y \left (x \right ) = \operatorname {DESol}\left (\left \{f \left (x \right ) \left (\frac {d^{3}}{d x^{3}}\textit {\_Y} \left (x \right )\right )+\left (\frac {d}{d x}f \left (x \right )+g \left (x \right )+A \left (x \right ) f \left (x \right )\right ) \left (\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right )+\left (\frac {d}{d x}g \left (x \right )+h \left (x \right )+A \left (x \right ) g \left (x \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )+\left (\frac {d}{d x}h \left (x \right )+A \left (x \right ) h \left (x \right )\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]