28.1.41 problem 42

Internal problem ID [4347]
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
Date solved : Monday, January 27, 2025 at 09:06:24 AM
CAS classification : [[_homogeneous, `class G`], _dAlembert]

\begin{align*} x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.079 (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)
 

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

✓ Solution by Mathematica

Time used: 0.659 (sec). Leaf size: 34

DSolve[(x-Sqrt[x^2+y[x]^2])+(y[x]-Sqrt[x^2+y[x]^2])*D[y[x],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*}