10.5.9 problem 9

Internal problem ID [1201]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:44:17 AM
CAS classification : [_exact]

\begin{align*} 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{align*}

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 35

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)
 

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

✓ Solution by Mathematica

Time used: 60.568 (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])*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-3 W\left (-\frac {1}{3} x e^{\frac {1}{3} x \left (x^2-c_1\right )} \cos (2 x)\right )+x^3-c_1 x}{3 x} \]