\[ a y'(x)^3+b y'(x)^2+c y'(x)-d-y(x)=0 \] ✓ Mathematica : cpu = 0.0280241 (sec), leaf count = 1124
DSolve[-d - y[x] + c*Derivative[1][y][x] + b*Derivative[1][y][x]^2 + a*Derivative[1][y][x]^3 == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}}}{2 b \sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}}+2^{2/3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}\right )^{2/3}+2 \sqrt [3]{2} b^2-6 \sqrt [3]{2} a c}d\text {$\#$1}\& \right ]\left [c_1-\frac {x}{6 a}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}}}{-4 b \sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}}+2^{2/3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}\right )^{2/3}-2^{2/3} i \sqrt {3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}\right )^{2/3}+2 \sqrt [3]{2} b^2-6 \sqrt [3]{2} a c+2 \sqrt [3]{2} b^2 i \sqrt {3}-6 \sqrt [3]{2} a c i \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {x}{12 a}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}}}{-4 b \sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}}+2^{2/3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}\right )^{2/3}+2^{2/3} i \sqrt {3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}+\sqrt {4 \left (3 a c-b^2\right )^3+\left (2 b^3-9 a c b-27 a^2 d-27 a^2 \text {$\#$1}\right )^2}\right )^{2/3}+2 \sqrt [3]{2} b^2-6 \sqrt [3]{2} a c-2 \sqrt [3]{2} b^2 i \sqrt {3}+6 \sqrt [3]{2} a c i \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {x}{12 a}+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.182 (sec), leaf count = 874
dsolve(a*diff(y(x),x)^3+b*diff(y(x),x)^2+c*diff(y(x),x)-y(x)-d=0,y(x))
\[x -\left (\int _{}^{y \left (x \right )}\frac {6 \,6^{\frac {1}{3}} a \left (12 \sqrt {3}\, \sqrt {27 \left (d +\textit {\_a} \right )^{2} a^{2}+18 \left (\left (d +\textit {\_a} \right ) b +\frac {2 c^{2}}{9}\right ) c a +\left (-4 d -4 \textit {\_a} \right ) b^{3}-b^{2} c^{2}}\, a +\left (108 d +108 \textit {\_a} \right ) a^{2}+36 b c a -8 b^{3}\right )^{\frac {1}{3}}}{6^{\frac {1}{3}} \left (12 \sqrt {3}\, \sqrt {27 \left (d +\textit {\_a} \right )^{2} a^{2}+18 \left (\left (d +\textit {\_a} \right ) b +\frac {2 c^{2}}{9}\right ) c a +\left (-4 d -4 \textit {\_a} \right ) b^{3}-b^{2} c^{2}}\, a +\left (108 d +108 \textit {\_a} \right ) a^{2}+36 b c a -8 b^{3}\right )^{\frac {2}{3}}-12 \,6^{\frac {1}{3}} a c +4 \,6^{\frac {1}{3}} b^{2}-4 b 27^{\frac {1}{3}} \left (\sqrt {3}\, \left (\frac {\sqrt {27 \left (d +\textit {\_a} \right )^{2} a^{2}+18 \left (\left (d +\textit {\_a} \right ) b +\frac {2 c^{2}}{9}\right ) c a +\left (-4 d -4 \textit {\_a} \right ) b^{3}-b^{2} c^{2}}\, a}{3}+\left (\left (d +\textit {\_a} \right ) a^{2}+\frac {b c a}{3}-\frac {2 b^{3}}{27}\right ) \sqrt {3}\right )\right )^{\frac {1}{3}}}d \textit {\_a} \right )-c_{1} = 0\]