Internal problem ID [551]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 40
dsolve(2*x-2*exp(x*y(x))*sin(2*x)+exp(x*y(x))*cos(2*x)*y(x)+(-3+exp(x*y(x))*x*cos(2*x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {-x^{3}-x c_{1}+3 \LambertW \left (-\frac {x \cos \left (2 x \right ) {\mathrm e}^{\frac {x^{3}}{3}} {\mathrm e}^{\frac {x c_{1}}{3}}}{3}\right )}{3 x} \]
✓ Solution by Mathematica
Time used: 0.464 (sec). Leaf size: 48
DSolve[2*x-2*Exp[x*y[x]]*Sin[2*x]+Exp[x*y[x]]*Cos[2*x]*y[x]+(-3+Exp[x*y[x]]*x*Cos[2*x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-3 \text {ProductLog}\left (-\frac {1}{3} x e^{\frac {1}{3} x \left (x^2-c_1\right )} \cos (2 x)\right )+x^3-c_1 x}{3 x} \\ \end{align*}