Internal problem ID [3782]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 530.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x \left (x +y\right ) y^{\prime }-\left (x +y\right ) y+x \sqrt {x^{2}-y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 42
dsolve(x*(x+y(x))*diff(y(x),x)-y(x)*(x+y(x))+x*sqrt(x^2-y(x)^2) = 0,y(x), singsol=all)
\[ \arctan \left (\frac {y \left (x \right )}{\sqrt {x^{2}-y \left (x \right )^{2}}}\right )-\frac {\sqrt {x^{2}-y \left (x \right )^{2}}}{x}+\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 109
DSolve[x(x+y[x])y'[x]-y[x](x+y[x])+x Sqrt[x^2-y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \sqrt {\frac {y(x)}{x}-1} \text {arctanh}\left (\frac {1}{\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}}\right )+\left (\frac {y(x)}{x}-1\right ) \sqrt {\frac {y(x)}{x}+1}}{\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}} \sqrt {\frac {y(x)}{x}+1}}=c_1-i \log (x),y(x)\right ] \]