Internal problem ID [8108]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 528.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+a \left (y^{\prime }\right )^{2}+b y+a b x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.264 (sec). Leaf size: 95
dsolve(diff(y(x),x)^3+a*diff(y(x),x)^2+b*y(x)+a*b*x=0,y(x), singsol=all)
\[ y \relax (x ) = -a x -\frac {\left ({\mathrm e}^{\RootOf \left (-2 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+8 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -5 a^{2}-2 b x \right )}-a \right )^{2} a +\left ({\mathrm e}^{\RootOf \left (-2 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+8 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -5 a^{2}-2 b x \right )}-a \right )^{3}}{b} \]
✓ Solution by Mathematica
Time used: 0.606 (sec). Leaf size: 398
DSolve[a*b*x + b*y[x] + a*y'[x]^2 + y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=-\frac {-a \left (\frac {\sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}-\frac {a}{3}\right )+\frac {3}{2} \left (\frac {\sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}-\frac {a}{3}\right )^2+a^2 \log \left (\frac {\sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{-2 a^3+\sqrt {\left (-2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {2 a}{3}\right )}{b}+c_1\right \},y(x)\right ] \]