28.1.135 problem 158

Internal problem ID [4441]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 158
Date solved : Monday, January 27, 2025 at 09:17:31 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 32

dsolve(x+sin(y(x)/x)^2*(y(x)-x*diff(y(x),x))=0,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: 0.370 (sec). Leaf size: 31

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

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