Internal problem ID [2904]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 156.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -a -b \,x^{n}-c y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 28
dsolve(x*diff(y(x),x) = a+b*x^n+c*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a}{c}+\frac {b \,x^{n}}{-c +n}+x^{c} c_{1} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 31
DSolve[x y'[x]==a+b x^n+c y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a}{c}-\frac {b x^n}{c-n}+c_1 x^c \\ \end{align*}