20.4.32 problem Problem 48

Internal problem ID [3667]
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
Date solved : Monday, January 27, 2025 at 07:53:02 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.013 (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)
 

\[ y \left (x \right ) = \left (\frac {x^{3}+c_{1}}{x}\right )^{-\frac {1}{\pi -1}} \]

✓ Solution by Mathematica

Time used: 1.237 (sec). Leaf size: 28

DSolve[D[y[x],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*}