Internal problem ID [14380]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime } t -y-\sqrt {y^{2}+t^{2}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 8.969 (sec). Leaf size: 21
dsolve([t*diff(y(t),t)-(y(t)+sqrt(t^2+y(t)^2))=0,y(1) = 0],y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {t^{2}}{2}+\frac {1}{2} \\ y \left (t \right ) &= \frac {t^{2}}{2}-\frac {1}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.346 (sec). Leaf size: 14
DSolve[{t*y'[t]-(y[t]+Sqrt[t^2+y[t]^2])==0,{y[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (t^2-1\right ) \]