74.7.37 problem 37

Internal problem ID [16114]
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
Date solved : Tuesday, January 28, 2025 at 08:42:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 1.082 (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 &= -\frac {t^{2}}{2}+\frac {1}{2} \\ y &= \frac {t^{2}}{2}-\frac {1}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.299 (sec). Leaf size: 14

DSolve[{t*D[y[t],t]-(y[t]+Sqrt[t^2+y[t]^2])==0,{y[1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} \left (t^2-1\right ) \]