Internal problem ID [3438]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 182.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {x y^{\prime }+\left (a +b \,x^{n} y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(x*diff(y(x),x)+(a+b*x^n*y(x))*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {a -n}{x^{a} c_{1} a -x^{a} c_{1} n -b \,x^{n}} \]
✓ Solution by Mathematica
Time used: 0.284 (sec). Leaf size: 36
DSolve[x y'[x]+(a+b x^n y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a-n}{-b x^n+c_1 (a-n) x^a} y(x)\to 0 \end{align*}