Internal problem ID [3116]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {x y^{\prime }-\sqrt {y^{2}+x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
dsolve(x*diff(y(x),x)=sqrt(x^2+y(x)^2),y(x), singsol=all)
\[ \frac {y \left (x \right )^{2}+y \left (x \right ) \sqrt {x^{2}+y \left (x \right )^{2}}+\left (\ln \left (y \left (x \right )+\sqrt {x^{2}+y \left (x \right )^{2}}\right )-c_{1} -3 \ln \left (x \right )\right ) x^{2}}{x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 66
DSolve[x*y'[x]==Sqrt[x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \left (\frac {y(x) \left (\sqrt {\frac {y(x)^2}{x^2}+1}+\frac {y(x)}{x}\right )}{x}-\log \left (\sqrt {\frac {y(x)^2}{x^2}+1}-\frac {y(x)}{x}\right )\right )=\log (x)+c_1,y(x)\right ] \]