Internal problem ID [2187]
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 48.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{\left (\pi -1\right ) x}-\frac {3 x y^{\pi }}{1-\pi }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 21
dsolve(diff(y(x),x)-1/( (Pi-1)*x)*y(x)=3/(1-Pi)*x*y(x)^Pi,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{3}+c_{1}}{x}\right )^{-\frac {1}{\pi -1}} \]
✓ Solution by Mathematica
Time used: 0.771 (sec). Leaf size: 28
DSolve[y'[x]-1/( (Pi-1)*x)*y[x]==3/(1-Pi)*x*y[x]^Pi,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {x^3+c_1}{x}\right ){}^{\frac {1}{1-\pi }} \\ y(x)\to 0 \\ \end{align*}