35.4.8 problem 8

Internal problem ID [6126]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:37:34 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 27

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

\[ \frac {-c_1 y^{2}+\sqrt {y^{2}+x^{2}}+x}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.398 (sec). Leaf size: 57

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

\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}