60.1.362 problem 363

Internal problem ID [10376]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 363
Date solved : Monday, January 27, 2025 at 07:38:05 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} \left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 32

dsolve((x*diff(y(x),x)-y(x))*cos(y(x)/x)^2+x = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 28

DSolve[x + Cos[y[x]/x]^2*(-y[x] + x*D[y[x],x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\cos ^2(K[1])dK[1]=-\log (x)+c_1,y(x)\right ] \]