78.4.7 problem 8

Internal problem ID [18130]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 11:30:44 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

dsolve((-1/y(x)*sin(x/y(x)) )+(x/y(x)^2*sin(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{\pi -c_1} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 19

DSolve[(-1/y[x]*Sin[x/y[x]])+(x/y[x]^2*Sin[x/y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x \\ y(x)\to \text {ComplexInfinity} \\ y(x)\to \text {ComplexInfinity} \\ \end{align*}