29.6.10 problem 156

Internal problem ID [4756]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 156
Date solved : Monday, January 27, 2025 at 09:36:32 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.616 (sec). Leaf size: 31

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

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