Internal problem ID [1045]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {{\mathrm e}^{y x} \left (y x^{4}+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve((exp(x*y(x))*(x^4*y(x)+4*x^3)+3*y(x))+( x^5*exp(x*y(x))+3*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3 \operatorname {LambertW}\left (\frac {x^{4} {\mathrm e}^{-\frac {c_{1}}{3}}}{3}\right )+c_{1}}{3 x} \]
✓ Solution by Mathematica
Time used: 4.266 (sec). Leaf size: 33
DSolve[(Exp[x*y[x]]*(x^4*y[x]+4*x^3)+3*y[x])+(x^5*Exp[x*y[x]]+3*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1-3 W\left (\frac {1}{3} e^{\frac {c_1}{3}} x^4\right )}{3 x} \\ \end{align*}