Internal problem ID [1680]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {t y^{\prime }-y-\sqrt {t^{2}+y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 1.719 (sec). Leaf size: 21
dsolve([t*diff(y(t),t)=y(t)+sqrt(t^2+y(t)^2),y(1) = 0],y(t), singsol=all)
\begin{align*} y \relax (t ) = -\frac {t^{2}}{2}+\frac {1}{2} \\ y \relax (t ) = \frac {t^{2}}{2}-\frac {1}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.362 (sec). Leaf size: 14
DSolve[{t*y'[t]==y[t]+Sqrt[t^2+y[t]^2],y[1]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (t^2-1\right ) \\ \end{align*}