Internal problem ID [3757]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1043.
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}-\left (y^{\prime }\right )^{2} a +b y+a b x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.146 (sec). Leaf size: 96
dsolve(diff(y(x),x)^3-a*diff(y(x),x)^2+b*y(x)+a*b*x = 0,y(x), singsol=all)
\[ y \relax (x ) = -a x +\frac {\left ({\mathrm e}^{\RootOf \left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -13 a^{2}-2 b x \right )}-a \right )^{2} a -\left ({\mathrm e}^{\RootOf \left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -13 a^{2}-2 b x \right )}-a \right )^{3}}{b} \]
✓ Solution by Mathematica
Time used: 0.658 (sec). Leaf size: 398
DSolve[(y'[x])^3 - a (y'[x])^2 +b y[x]+a b x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {5 a \left (\frac {\sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {a}{3}\right )-\frac {3}{2} \left (\frac {\sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {a}{3}\right )^2-5 a^2 \log \left (\frac {\sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {4 a}{3}\right )}{b}+c_1\right \},y(x)\right ] \]