75.5.5 problem 104

Internal problem ID [16741]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 104
Date solved : Tuesday, January 28, 2025 at 09:20:32 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 14

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

\[ y(x)\to -x \cosh (\log (x)+c_1) \]