15.2.19 problem 19

Internal problem ID [2889]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 19
Date solved : Monday, January 27, 2025 at 06:25:06 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (6\right )&=\pi \end{align*}

✓ Solution by Maple

Time used: 0.134 (sec). Leaf size: 10

dsolve([diff(y(x),x)=y(x)/x+tan(y(x)/x),y(6) = Pi],y(x), singsol=all)
 

\[ y = \arcsin \left (\frac {x}{12}\right ) x \]

✓ Solution by Mathematica

Time used: 9.007 (sec). Leaf size: 13

DSolve[{D[y[x],x]==y[x]/x+Tan[y[x]/x],y[6]==Pi},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \arcsin \left (\frac {x}{12}\right ) \]