75.5.1 problem 100

Internal problem ID [16737]
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 : 100
Date solved : Tuesday, January 28, 2025 at 09:20:19 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y+x \cos \left (\frac {y}{x}\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

dsolve(x*diff(y(x),x)=y(x)+x*cos(y(x)/x)^2,y(x), singsol=all)
 

\[ y = \arctan \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.426 (sec). Leaf size: 35

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

\begin{align*} y(x)\to x \arctan (\log (x)+2 c_1) \\ y(x)\to -\frac {\pi x}{2} \\ y(x)\to \frac {\pi x}{2} \\ \end{align*}