78.8.32 problem 32

Internal problem ID [18230]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 11:42:15 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 26

dsolve(3*y(x)^2/(x^2+3*x) + (2*y(x)*ln( 5*x/(x+3) ) +3*sin(y(x)) ) * diff(y(x),x)=0,y(x), singsol=all)
 

\[ \left (\ln \left (5\right )+\ln \left (\frac {x}{x +3}\right )\right ) y^{2}-3 \cos \left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.414 (sec). Leaf size: 64

DSolve[3*y[x]^2/(x^2+3*x) + (2*y[x]*Log[ 5*x/(x+3) ] +3*Sin[y[x]] ) *D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [y(x)^2 (-\log (x))+y(x)^2 \log \left (\frac {5 x}{x+3}\right )+3 y(x)^2 \left (\frac {\log (x)}{3}-\frac {1}{3} \log (x+3)\right )+y(x)^2 \log (x+3)-3 \cos (y(x))=c_1,y(x)\right ] \]