8.5.14 problem 14

Internal problem ID [742]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 14
Date solved : Wednesday, February 05, 2025 at 03:57:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 27

dsolve(x+y(x)*diff(y(x),x) = (x^2+y(x)^2)^(1/2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.358 (sec). Leaf size: 57

DSolve[x+y[x]*D[y[x],x] == (x^2+y[x]^2)^(1/2),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*}