\[ x y^{(3)}(x) (a x+b)+(\alpha x+\beta ) y''(x)-f(x)+x y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 3.62287 (sec), leaf count = 70099
DSolve[-f[x] + y[x] + x*Derivative[1][y][x] + (beta + alpha*x)*Derivative[2][y][x] + x*(b + a*x)*Derivative[3][y][x] == 0,y[x],x]
\[ \text {Too large to display} \] ✓ Maple : cpu = 0.663 (sec), leaf count = 1209
dsolve((a*x+b)*x*diff(diff(diff(y(x),x),x),x)+(alpha*x+beta)*diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x)-f(x)=0,y(x))
\[y \left (x \right ) = -\left (\left (\left (\int \frac {\HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) \left (a x +b \right )^{\frac {\left (-3 b -\beta \right ) a +\alpha b}{a b}} \left (c_{1}+\int f \left (x \right )d x \right ) x^{\frac {-2 b +\beta }{b}}}{\left (\left (-2 b +\beta \right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )-a \HeunCPrime \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) x \right ) \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )+\HeunCPrime \left (0, \frac {2 b -\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) x a}d x \right ) b -c_{2}\right ) \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) x^{\frac {2 b -\beta }{b}}-\left (\left (\int \frac {\left (a x +b \right )^{\frac {\left (-3 b -\beta \right ) a +\alpha b}{a b}} \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) \left (c_{1}+\int f \left (x \right )d x \right )}{\left (\left (-2 b +\beta \right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )-a \HeunCPrime \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) x \right ) \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )+\HeunCPrime \left (0, \frac {2 b -\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) x a}d x \right ) b +c_{3}\right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {\left (2 b +\beta \right ) a -\alpha b}{a b}, -\frac {b}{a^{2}}, \frac {\left (4 a -\alpha \right ) b^{2}-\alpha \beta b +a \,\beta ^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )\right ) \left (a x +b \right )^{\frac {\left (2 b +\beta \right ) a -\alpha b}{a b}}\]