\[ \boxed { a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}+b \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+c{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) -d=0} \]
Mathematica: cpu = 3505.56 (sec), leaf count = 1258 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {\sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 K[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 K[1]\right )^2}}}{2 b \sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 K[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 K[1]\right )^2}}+2^{2/3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 K[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 K[1]\right )^2}\right )^{2/3}+2 \sqrt [3]{2} b^2-6 \sqrt [3]{2} a c} \, dK[1]\& \right ]\left [c_1-\frac {x}{6 a}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {\sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 K[2]+\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 K[2]\right )^2}}}{-4 b \sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 K[2]+\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 K[2]\right )^2}}+2^{2/3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 K[2]+\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 K[2]\right )^2}\right )^{2/3}-i 2^{2/3} \sqrt {3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 K[2]+\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 K[2]\right )^2}\right )^{2/3}+2 \sqrt [3]{2} b^2-6 \sqrt [3]{2} a c-6 i \sqrt [3]{2} \sqrt {3} a c+2 \sqrt [3]{2} \sqrt {3} b^2 i} \, dK[2]\& \right ]\left [\frac {x}{12 a}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {\sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 K[3]+\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 K[3]\right )^2}}}{-4 b \sqrt [3]{2 b^3-9 a c b-27 a^2 d-27 a^2 K[3]+\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 K[3]\right )^2}}+2^{2/3} \left (2 b^3-9 a c b-27 a^2 d-27 a^2 K[3]+\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 K[3]\right )^2}\right )^{2/3}+2^{2/3} \sqrt {3} i \left (2 b^3-9 a c b-27 a^2 d-27 a^2 K[3]+\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 K[3]\right )^2}\right )^{2/3}+2 \sqrt [3]{2} b^2-2 i \sqrt [3]{2} \sqrt {3} b^2-6 \sqrt [3]{2} a c+6 \sqrt [3]{2} \sqrt {3} a c i} \, dK[3]\& \right ]\left [\frac {x}{12 a}+c_1\right ]\right \}\right \} \]
Maple: cpu = 0.125 (sec), leaf count = 1211 \[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {a\sqrt [3]{108\,{ \it \_a}\,{a}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{ \it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2 }{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2 }d+36\,abc-8\,{b}^{3}}}{ \left ( 108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3} \sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a }\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4 \,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3} \right ) ^ {2/3}-2\,b\sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3}\sqrt {27\,{{ \it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{ \it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d- {b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}-12\,ac+4\,{b}^{2}}} {d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {a \sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^ {2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b }^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{ 2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}}{ \left ( i\sqrt {3}-1 \right ) \left ( i\sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3}\sqrt {27\,{{ \it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4\,{ \it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3}d- {b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}\sqrt {3}b-6\,i \sqrt {3}ac+2\,i\sqrt {3}{b}^{2}+ \left ( 108\,{\it \_a}\,{a}^{2}+12\, \sqrt {3}\sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18 \,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\, a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3} \right ) ^{2/3}+b\sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc -4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^ {3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}+6\,ac-2\,{b}^{ 2} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\! 12\,{\frac {a\sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3}\sqrt {27 \,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a}\,abc-4 \,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4\,{b}^{3 }d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}}{ \left ( i\sqrt {3}+1 \right ) \left ( i\sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3} \sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a }\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4 \,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}\sqrt {3} b-6\,i\sqrt {3}ac+2\,i\sqrt {3}{b}^{2}- \left ( 108\,{\it \_a}\,{a}^{2} +12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2} d+18\,{\it \_a}\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd +4\,a{c}^{3}-4\,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b} ^{3} \right ) ^{2/3}-b\sqrt [3]{108\,{\it \_a}\,{a}^{2}+12\,\sqrt {3} \sqrt {27\,{{\it \_a}}^{2}{a}^{2}+54\,{\it \_a}\,{a}^{2}d+18\,{\it \_a }\,abc-4\,{\it \_a}\,{b}^{3}+27\,{a}^{2}{d}^{2}+18\,abcd+4\,a{c}^{3}-4 \,{b}^{3}d-{b}^{2}{c}^{2}}a+108\,{a}^{2}d+36\,abc-8\,{b}^{3}}-6\,ac+2 \,{b}^{2} \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \]