Internal problem ID [2179]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 y}{2 x}-6 y^{\frac {1}{3}} x^{2} \ln \relax (x )=0} \end {gather*}
✓ 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)
\[ -2 x^{3} \ln \relax (x )+x^{3}+y \relax (x )^{\frac {2}{3}}-x c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.384 (sec). Leaf size: 26
DSolve[y'[x]-3/(2*x)*y[x]==6*y[x]^(1/3)*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x \left (-x^2+2 x^2 \log (x)+c_1\right )\right ){}^{3/2} \\ \end{align*}