20.4.14 problem Problem 22

Internal problem ID [3649]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 22
Date solved : Monday, January 27, 2025 at 07:50:03 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

dsolve(x*diff(y(x),x)=x*tan(y(x)/x)+y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \arcsin \left (c_{1} x \right ) x \]

✓ Solution by Mathematica

Time used: 9.296 (sec). Leaf size: 19

DSolve[x*D[y[x],x]==x*Tan[y[x]/x]+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \arcsin \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}