Internal problem ID [2720]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 87.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+y^{2}-y y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.391 (sec). Leaf size: 309
dsolve((diff(y(x),x))^3+y(x)^2=x*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -\frac {\sqrt {-2 x^{5} \sqrt {x^{2}+3 c_{1}}+2 x^{6}+12 x^{3} c_{1} \sqrt {x^{2}+3 c_{1}}-9 x^{4} c_{1}+54 x c_{1}^{2} \sqrt {x^{2}+3 c_{1}}+108 x^{2} c_{1}^{2}+27 c_{1}^{3}}}{27} \\ y \relax (x ) = \frac {\sqrt {-2 x^{5} \sqrt {x^{2}+3 c_{1}}+2 x^{6}+12 x^{3} c_{1} \sqrt {x^{2}+3 c_{1}}-9 x^{4} c_{1}+54 x c_{1}^{2} \sqrt {x^{2}+3 c_{1}}+108 x^{2} c_{1}^{2}+27 c_{1}^{3}}}{27} \\ y \relax (x ) = -\frac {\sqrt {2 x^{5} \sqrt {x^{2}+3 c_{1}}+2 x^{6}-12 x^{3} c_{1} \sqrt {x^{2}+3 c_{1}}-9 x^{4} c_{1}-54 x c_{1}^{2} \sqrt {x^{2}+3 c_{1}}+108 x^{2} c_{1}^{2}+27 c_{1}^{3}}}{27} \\ y \relax (x ) = \frac {\sqrt {2 x^{5} \sqrt {x^{2}+3 c_{1}}+2 x^{6}-12 x^{3} c_{1} \sqrt {x^{2}+3 c_{1}}-9 x^{4} c_{1}-54 x c_{1}^{2} \sqrt {x^{2}+3 c_{1}}+108 x^{2} c_{1}^{2}+27 c_{1}^{3}}}{27} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3+y[x]^2==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
Timed out