56.4.33 problem 29

Internal problem ID [8922]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 03:55:55 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} \left (y-2 x y^{\prime }\right )^{2}&={y^{\prime }}^{3} \end{align*}

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 73

dsolve((y(x)-2*x*diff(y(x),x))^2= diff(y(x),x)^3,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ \left [x \left (\textit {\_T} \right ) &= \frac {3 \textit {\_T}^{{5}/{2}}+5 c_{1}}{5 \textit {\_T}^{2}}, y \left (\textit {\_T} \right ) = \frac {\textit {\_T}^{{5}/{2}}+10 c_{1}}{5 \textit {\_T}}\right ] \\ \left [x \left (\textit {\_T} \right ) &= \frac {-3 \textit {\_T}^{{5}/{2}}+5 c_{1}}{5 \textit {\_T}^{2}}, y \left (\textit {\_T} \right ) = \frac {-\textit {\_T}^{{5}/{2}}+10 c_{1}}{5 \textit {\_T}}\right ] \\ \end{align*}

✓ Solution by Mathematica

Time used: 91.539 (sec). Leaf size: 32354

DSolve[(y[x]-2*x*D[y[x],x])^2== D[y[x],x]^3,y[x],x,IncludeSingularSolutions -> True]
 

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