29.14.2 problem 381

Internal problem ID [4981]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 381
Date solved : Monday, January 27, 2025 at 10:00:56 AM
CAS classification : [_linear]

\begin{align*} x^{n} y^{\prime }&=a +b \,x^{n -1} y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(x^n*diff(y(x),x) = a+b*x^(n-1)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {a \,x^{1-n}}{n +b -1}+x^{b} c_{1} \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 28

DSolve[x^n D[y[x],x]==a+b x^(n-1) y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {a x^{1-n}}{b+n-1}+c_1 x^b \]