5.14 problem 14

Internal problem ID [92]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]

\[ \boxed {y y^{\prime }-\sqrt {x^{2}+y^{2}}=-x} \]

Solution by Maple

Time used: 0.031 (sec). Leaf size: 28

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

\[ -c_{1} +\frac {\sqrt {x^{2}+y \left (x \right )^{2}}}{y \left (x \right )^{2}}+\frac {x}{y \left (x \right )^{2}} = 0 \]

Solution by Mathematica

Time used: 0.402 (sec). Leaf size: 57

DSolve[x+y[x]*y'[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*}