15.8.29 problem 30

Internal problem ID [3032]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 30
Date solved : Monday, January 27, 2025 at 07:09:38 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 29

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

\[ \frac {-c_{1} y+\sqrt {x^{2}+y^{2}}\, x +x^{2}}{y} = 0 \]

✓ Solution by Mathematica

Time used: 0.325 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -x \sqrt {-\text {sech}^2(\log (x)+c_1)} \\ y(x)\to x \sqrt {-\text {sech}^2(\log (x)+c_1)} \\ y(x)\to 0 \\ \end{align*}