22.1.3 problem 3

Internal problem ID [4089]
Book : Applied Differential equations, Newby Curle. Van Nostrand Reinhold. 1972
Section : Examples, page 35
Problem number : 3
Date solved : Monday, January 27, 2025 at 08:08:19 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y-x&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 49

dsolve(y(x)-x=(diff(y(x),x))^2*(1-2/3* diff(y(x),x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 176.550 (sec). Leaf size: 14234

DSolve[y[x]-x==D[y[x],x]^2*(1-2/3* D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

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