20.4.24 problem Problem 40

Internal problem ID [3659]
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 40
Date solved : Monday, January 27, 2025 at 07:52:39 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(x),x)-3/(2*x)*y(x)=6*y(x)^(1/3)*x^2*ln(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.836 (sec). Leaf size: 26

DSolve[D[y[x],x]-3/(2*x)*y[x]==6*y[x]^(1/3)*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x \left (-x^2+2 x^2 \log (x)+c_1\right )\right ){}^{3/2} \]