Internal problem ID [2184]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {6 y}{x}-\frac {3 y^{\frac {2}{3}} \cos \relax (x )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)+6/x*y(x)=3/x*y(x)^(2/3)*cos(x),y(x), singsol=all)
\[ y \relax (x )^{\frac {1}{3}}-\frac {\cos \relax (x )+\sin \relax (x ) x +c_{1}}{x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 20
DSolve[y'[x]+6/x*y[x]==3/x*y[x]^(2/3)*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(x \sin (x)+\cos (x)+c_1){}^3}{x^6} \\ \end{align*}