7.5.14 problem 14

Internal problem ID [118]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 14
Date solved : Friday, February 07, 2025 at 07:52:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 27

dsolve(y(x)*diff(y(x),x)+x=sqrt(x^2+y(x)^2),y(x), singsol=all)
 

\[ \frac {-c_1 y^{2}+\sqrt {x^{2}+y^{2}}+x}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.411 (sec). Leaf size: 57

DSolve[y[x]*D[y[x],x]+x==Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ \end{align*}