20.4.29 problem Problem 45

Internal problem ID [3664]
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
Date solved : Monday, January 27, 2025 at 07:52:55 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x)+6/x*y(x)=3/x*y(x)^(2/3)*cos(x),y(x), singsol=all)
 

\[ \frac {y \left (x \right )^{{1}/{3}} x^{2}-x \sin \left (x \right )-\cos \left (x \right )-c_{1}}{x^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 20

DSolve[D[y[x],x]+6/x*y[x]==3/x*y[x]^(2/3)*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(x \sin (x)+\cos (x)+c_1){}^3}{x^6} \]