60.1.417 problem 419

Internal problem ID [10431]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 419
Date solved : Monday, January 27, 2025 at 07:43:39 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x {y^{\prime }}^{2}+2 y^{\prime } y-x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 111

dsolve(x*diff(y(x),x)^2+2*y(x)*diff(y(x),x)-x = 0,y(x), singsol=all)
 

\begin{align*} x -\frac {2^{{1}/{3}} \left (\sqrt {x^{2}+y^{2}}-y\right ) c_{1}}{2 \left (\frac {3 y^{2}-3 y \sqrt {x^{2}+y^{2}}+x^{2}}{x^{2}}\right )^{{2}/{3}} x} &= 0 \\ \frac {c_{1} \left (\sqrt {x^{2}+y^{2}}+y\right )}{{\left (\frac {3 y \sqrt {x^{2}+y^{2}}+x^{2}+3 y^{2}}{x^{2}}\right )}^{{2}/{3}} x}+x &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.651 (sec). Leaf size: 6977

DSolve[-x + 2*y[x]*D[y[x],x] + x*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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