40.2.8 problem 31

Internal problem ID [6586]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 31
Date solved : Monday, January 27, 2025 at 02:14:20 PM
CAS classification : [[_homogeneous, `class G`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 60

dsolve(y(x)*sqrt(x^2+y(x)^2)-x*(x+sqrt(x^2+y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \frac {x \ln \left (\frac {x \left (x +\sqrt {x^{2}+y^{2}}\right )}{y}\right )-\ln \left (x \right ) x +x \ln \left (2\right )-\ln \left (y\right ) x -c_1 x -\sqrt {x^{2}+y^{2}}}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 43

DSolve[y[x]*Sqrt[x^2+y[x]^2]-x*(x+Sqrt[x^2+y[x]^2])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\sqrt {\frac {y(x)^2}{x^2}+1}+\log \left (\sqrt {\frac {y(x)^2}{x^2}+1}-1\right )=-\log (x)+c_1,y(x)\right ] \]