29.8.1 problem 206

Internal problem ID [4806]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 206
Date solved : Monday, January 27, 2025 at 09:40:16 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.074 (sec). Leaf size: 31

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

\[ \frac {x \sin \left (\frac {2 y \left (x \right )}{x}\right )+2 y \left (x \right )}{4 x}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.283 (sec). Leaf size: 31

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

\[ \text {Solve}\left [\frac {y(x)}{2 x}+\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=\log (x)+c_1,y(x)\right ] \]