83.4.7 problem 7

Internal problem ID [19079]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:52:21 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 3.053 (sec). Leaf size: 19

DSolve[D[y[x],x]==y[x]/x+Tan[y[x]/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*}