4.8 problem 8

Internal problem ID [4274]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]

Solve \begin {gather*} \boxed {y y^{\prime }+x -\sqrt {x^{2}+y^{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.044 (sec). Leaf size: 28

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

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

Solution by Mathematica

Time used: 0.377 (sec). Leaf size: 57

DSolve[y[x]*y'[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*}