Internal problem ID [3186]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _dAlembert]
\[ \boxed {-\sqrt {y^{2}+x^{2}}+\left (y-\sqrt {y^{2}+x^{2}}\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 47
dsolve((x-sqrt(x^2+y(x)^2))+(y(x)-sqrt(x^2+y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {\left (x +y \left (x \right )\right ) \sqrt {x^{2}+y \left (x \right )^{2}}+\left (-c_{1} x^{2}+1\right ) y \left (x \right )^{2}+x y \left (x \right )+x^{2}}{y \left (x \right )^{2} x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.834 (sec). Leaf size: 34
DSolve[(x-Sqrt[x^2+y[x]^2])+(y[x]-Sqrt[x^2+y[x]^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{c_1} \left (2 x+e^{c_1}\right )}{2 \left (x+e^{c_1}\right )} \\ y(x)\to 0 \\ \end{align*}