Internal problem ID [14369]
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: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y+2 \sqrt {y^{2}+t^{2}}-y^{\prime } t=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve((y(t)+2*sqrt(t^2+y(t)^2))-(t)*diff(y(t),t)=0,y(t), singsol=all)
\[ \frac {-c_{1} t^{3}+\sqrt {t^{2}+y \left (t \right )^{2}}+y \left (t \right )}{t^{3}} = 0 \]
✓ Solution by Mathematica
Time used: 0.25 (sec). Leaf size: 28
DSolve[(y[t]+2*Sqrt[t^2+y[t]^2])-(t)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {e^{-c_1}-e^{c_1} t^4}{2 t} \]