\[ x y^{(3)}(x) (a x+b)+(\alpha x+\beta ) y''(x)-f(x)+x y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 5.8388 (sec), leaf count = 70099 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.747 (sec), leaf count = 1210
\[\left \{y \left (x \right ) = \left (\left (b \left (\int -\frac {\left (c_{1}+\int f \left (x \right )d x \right ) x^{\frac {-2 b +\beta }{b}} \left (a x +b \right )^{\frac {\alpha b +\left (-3 b -\beta \right ) a}{a b}} \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )}{a x \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) \HeunCPrime \left (0, \frac {2 b -\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )+\left (-a x \HeunCPrime \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )+\left (-2 b +\beta \right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )\right ) \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )}d x \right )+c_{2}\right ) x^{\frac {2 b -\beta }{b}} \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )-\left (b \left (\int -\frac {\left (c_{1}+\int f \left (x \right )d x \right ) \left (a x +b \right )^{\frac {\alpha b +\left (-3 b -\beta \right ) a}{a b}} \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )}{a x \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right ) \HeunCPrime \left (0, \frac {2 b -\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )+\left (-a x \HeunCPrime \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )+\left (-2 b +\beta \right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )\right ) \HeunC \left (0, \frac {2 b -\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )}d x \right )-c_{3}\right ) \HeunC \left (0, \frac {-2 b +\beta }{b}, \frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}, -\frac {b}{a^{2}}, \frac {a \,\beta ^{2}-\alpha b \beta +\left (4 a -\alpha \right ) b^{2}}{2 a \,b^{2}}, -\frac {a x}{b}\right )\right ) \left (a x +b \right )^{\frac {-\alpha b +\left (2 b +\beta \right ) a}{a b}}\right \}\]