28.1.78 problem 81

Internal problem ID [4384]
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 : 81
Date solved : Monday, January 27, 2025 at 09:09:46 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }+{y^{\prime }}^{3} \end{align*}

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 37

dsolve(y(x)=x*diff(y(x),x)+(diff(y(x),x))^3,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {2 \sqrt {3}\, \left (-x \right )^{{3}/{2}}}{9} \\ y \left (x \right ) &= -\frac {2 \sqrt {3}\, \left (-x \right )^{{3}/{2}}}{9} \\ y \left (x \right ) &= c_{1} \left (c_{1}^{2}+x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 54

DSolve[y[x]==x*D[y[x],x]+(D[y[x],x])^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \left (x+c_1{}^2\right ) \\ y(x)\to -\frac {2 i x^{3/2}}{3 \sqrt {3}} \\ y(x)\to \frac {2 i x^{3/2}}{3 \sqrt {3}} \\ \end{align*}