Internal problem ID [2173]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y-\sqrt {x^{2}+y^{2}}}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 21
dsolve([diff(y(x),x)=(y(x)-sqrt(x^2+y(x)^2))/x,y(3) = 4],y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2}}{2}-\frac {1}{2} \\ y \relax (x ) = -\frac {x^{2}}{18}+\frac {9}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 28
DSolve[{y'[x]==(y[x]-Sqrt[x^2+y[x]^2])/x,{y[3]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{18} (x-9) (x+9) \\ y(x)\to \frac {1}{2} \left (x^2-1\right ) \\ \end{align*}