74.7.26 problem 26

Internal problem ID [16103]
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
Date solved : Tuesday, January 28, 2025 at 08:41:03 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y+2 \sqrt {t^{2}+y^{2}}-y^{\prime } t&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

dsolve((y(t)+2*sqrt(t^2+y(t)^2))-(t)*diff(y(t),t)=0,y(t), singsol=all)
 

\[ \frac {-c_{1} t^{3}+\sqrt {t^{2}+y^{2}}+y}{t^{3}} = 0 \]

✓ Solution by Mathematica

Time used: 0.199 (sec). Leaf size: 15

DSolve[(y[t]+2*Sqrt[t^2+y[t]^2])-(t)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t \sinh (2 \log (t)+c_1) \]