12.6.16 problem 16

Internal problem ID [1695]
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
Date solved : Monday, January 27, 2025 at 05:29:39 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} {\mathrm e}^{y x} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

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)
 

\[ y = \frac {-3 \operatorname {LambertW}\left (\frac {x^{4} {\mathrm e}^{-\frac {c_1}{3}}}{3}\right )-c_1}{3 x} \]

✓ Solution by Mathematica

Time used: 4.187 (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)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1-3 W\left (\frac {1}{3} e^{\frac {c_1}{3}} x^4\right )}{3 x} \]