78.4.18 problem 19

Internal problem ID [18141]
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 : 19
Date solved : Tuesday, January 28, 2025 at 11:32:49 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} 3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 43

dsolve((3*x^2*(1+ln(y(x)))) +( x^3/y(x)-2*y(x) )*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x^{3} \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{\frac {-2 x^{3}-2 c_1}{x^{3}}}}{x^{3}}\right )+2 x^{3}+2 c_1}{2 x^{3}}} \]

✓ Solution by Mathematica

Time used: 60.172 (sec). Leaf size: 79

DSolve[(3*x^2*(1+Log[y[x]])) +( x^3/y[x]-2*y[x] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i x^{3/2} \sqrt {W\left (-\frac {2 e^{-2+\frac {2 c_1}{x^3}}}{x^3}\right )}}{\sqrt {2}} \\ y(x)\to \frac {i x^{3/2} \sqrt {W\left (-\frac {2 e^{-2+\frac {2 c_1}{x^3}}}{x^3}\right )}}{\sqrt {2}} \\ \end{align*}