\[ \text {a0} x+y'(x) (\text {a1} x+\text {b1} y(x)+\text {c1})+(\text {a2} x+\text {c2}) y'(x)^2+\text {b0} y(x)+\text {c0}=0 \] ✓ Mathematica : cpu = 218.475 (sec), leaf count = 507
DSolve[c0 + a0*x + b0*y[x] + (c1 + a1*x + b1*y[x])*Derivative[1][y][x] + (c2 + a2*x)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\text {Solve}\left [\left \{x=(\text {b1} K[1]+\text {b0}) \exp \left (\frac {(\text {b1} (\text {b0}-\text {a1})+2 \text {a2} \text {b0}) \arctan \left (\frac {2 (\text {a2}+\text {b1}) K[1]+\text {a1}+\text {b0}}{\sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {a2}+\text {b1}) \sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}-\frac {(2 \text {a2}+\text {b1}) \log (K[1] ((\text {a2}+\text {b1}) K[1]+\text {a1}+\text {b0})+\text {a0})}{2 (\text {a2}+\text {b1})}\right ) \left (\int \frac {\left (\frac {-2 \text {c2} K[1]-\text {c1}}{\text {b1} K[1]+\text {b0}}-\frac {\text {b1} \left (-\text {c1} K[1]-\text {c2} K[1]^2-\text {c0}\right )}{(\text {b1} K[1]+\text {b0})^2}\right ) \exp \left (\frac {(2 \text {a2}+\text {b1}) \log (K[1] ((\text {a2}+\text {b1}) K[1]+\text {a1}+\text {b0})+\text {a0})}{2 (\text {a2}+\text {b1})}-\frac {(\text {b1} (\text {b0}-\text {a1})+2 \text {a2} \text {b0}) \arctan \left (\frac {2 (\text {a2}+\text {b1}) K[1]+\text {a1}+\text {b0}}{\sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {a2}+\text {b1}) \sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {b1} K[1]+\text {b0}) \left (K[1]-\frac {-\text {a1} K[1]-\text {a2} K[1]^2-\text {a0}}{\text {b1} K[1]+\text {b0}}\right )} \, dK[1]\right )+c_1 (\text {b1} K[1]+\text {b0}) \exp \left (\frac {(\text {b1} (\text {b0}-\text {a1})+2 \text {a2} \text {b0}) \arctan \left (\frac {2 (\text {a2}+\text {b1}) K[1]+\text {a1}+\text {b0}}{\sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}\right )}{(\text {a2}+\text {b1}) \sqrt {4 \text {a0} (\text {a2}+\text {b1})-\text {a1}^2-2 \text {a1} \text {b0}-\text {b0}^2}}-\frac {(2 \text {a2}+\text {b1}) \log (K[1] ((\text {a2}+\text {b1}) K[1]+\text {a1}+\text {b0})+\text {a0})}{2 (\text {a2}+\text {b1})}\right ),y(x)=\frac {x \left (-\text {a1} K[1]-\text {a2} K[1]^2-\text {a0}\right )}{\text {b1} K[1]+\text {b0}}+\frac {-\text {c1} K[1]-\text {c2} K[1]^2-\text {c0}}{\text {b1} K[1]+\text {b0}}\right \},\{y(x),K[1]\}\right ]\] ✓ Maple : cpu = 2.454 (sec), leaf count = 1602
dsolve((a2*x+c2)*diff(y(x),x)^2+(a1*x+b1*y(x)+c1)*diff(y(x),x)+a0*x+b0*y(x)+c0 = 0,y(x))
\[\text {Expression too large to display}\]