20.4.18 problem Problem 27

Internal problem ID [3653]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 27
Date solved : Monday, January 27, 2025 at 07:51:10 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (3\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.365 (sec). Leaf size: 21

dsolve([diff(y(x),x)=(y(x)-sqrt(x^2+y(x)^2))/x,y(3) = 4],y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2}-\frac {1}{2} \\ y \left (x \right ) &= -\frac {x^{2}}{18}+\frac {9}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 16

DSolve[{D[y[x],x]==(y[x]-Sqrt[x^2+y[x]^2])/x,{y[3]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {9}{2}-\frac {x^2}{18} \]