\[ a x y(x)^2+b y(x)+c x+d+x y'(x)=0 \] ✓ Mathematica : cpu = 0.243652 (sec), leaf count = 473
\[\left \{\left \{y(x)\to \frac {c_1 \left (i \sqrt {a} e^{-i \sqrt {a} \sqrt {c} x} \left (b \left (-\sqrt {c}\right )-i \sqrt {a} d\right ) U\left (1-\frac {-\sqrt {c} b-i \sqrt {a} d}{2 \sqrt {c}},b+1,2 i \sqrt {a} \sqrt {c} x\right )-i \sqrt {a} \sqrt {c} e^{-i \sqrt {a} \sqrt {c} x} U\left (-\frac {-\sqrt {c} b-i \sqrt {a} d}{2 \sqrt {c}},b,2 i \sqrt {a} \sqrt {c} x\right )\right )-i \sqrt {a} \sqrt {c} e^{-i \sqrt {a} \sqrt {c} x} L_{\frac {-\sqrt {c} b-i \sqrt {a} d}{2 \sqrt {c}}}^{b-1}\left (2 i \sqrt {a} \sqrt {c} x\right )-2 i \sqrt {a} \sqrt {c} e^{-i \sqrt {a} \sqrt {c} x} L_{\frac {-\sqrt {c} b-i \sqrt {a} d}{2 \sqrt {c}}-1}^b\left (2 i \sqrt {a} \sqrt {c} x\right )}{a \left (c_1 e^{-i \sqrt {a} \sqrt {c} x} U\left (-\frac {-\sqrt {c} b-i \sqrt {a} d}{2 \sqrt {c}},b,2 i \sqrt {a} \sqrt {c} x\right )+e^{-i \sqrt {a} \sqrt {c} x} L_{\frac {-\sqrt {c} b-i \sqrt {a} d}{2 \sqrt {c}}}^{b-1}\left (2 i \sqrt {a} \sqrt {c} x\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.245 (sec), leaf count = 844
\[\left \{y \left (x \right ) = -\frac {4 \left (\left (\left (a d +\sqrt {-a c}\, b \right ) a \,c^{3} \KummerM \left (\frac {a b \,c^{2}+2 \sqrt {-a c}\, a c d +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )+\left (a d -\sqrt {-a c}\, b \right ) a \,c^{3} \KummerM \left (\frac {\left (\left (b +2\right ) c +2 \sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )-\frac {c_{1} \left (b c -\sqrt {-a c}\, d \right ) \KummerU \left (\frac {a b \,c^{2}+2 \sqrt {-a c}\, a c d +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )}{2}\right ) a^{2} c^{2}-\frac {c_{1} \left (a^{3} c^{2} d^{2}+a^{2} b^{2} c^{3}-2 \left (-a c \right )^{\frac {3}{2}} a b c d -2 \left (-a c \right )^{\frac {5}{2}} b d \right ) \KummerU \left (\frac {\left (\left (b +2\right ) c +2 \sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )}{4}\right ) c^{2}}{4 \left (\left (b c -\sqrt {-a c}\, d \right ) a^{2} c^{2} \KummerM \left (\frac {a b \,c^{2}+2 \sqrt {-a c}\, a c d +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )+\left (b c +\sqrt {-a c}\, d \right ) a^{2} c^{2} \KummerM \left (\frac {\left (\left (b +2\right ) c +2 \sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )+\frac {c_{1} \left (a d +\sqrt {-a c}\, b \right ) \KummerU \left (\frac {a b \,c^{2}+2 \sqrt {-a c}\, a c d +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )}{2}\right ) a^{2} c^{4}-c_{1} \left (\sqrt {-a c}\, a^{2} b^{2} c^{4}+2 \left (-a c \right )^{\frac {5}{2}} a c \,d^{2}+\left (-a c \right )^{\frac {7}{2}} d^{2}\right ) \KummerU \left (\frac {\left (\left (b +2\right ) c +2 \sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{2 a \,c^{2}}, \frac {\left (\left (b +1\right ) c +\sqrt {-a c}\, d \right ) a c +\left (-a c \right )^{\frac {3}{2}} d}{a \,c^{2}}, 2 \sqrt {-a c}\, x \right )}\right \}\]