Internal problem ID [3457]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 719.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (a +x y^{n}\right ) y^{\prime }+b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.145 (sec). Leaf size: 39
dsolve(x*(a+x*y(x)^n)*diff(y(x),x)+b*y(x) = 0,y(x), singsol=all)
\[ \left (x y \relax (x )^{n}-b n +a \right )^{b n} \left (y \relax (x )^{n}\right )^{-a} x^{-b n}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.272 (sec). Leaf size: 61
DSolve[x(a+x y[x]^n)y'[x]+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {a n \log (a y(x)-b n y(x))}{a-b n}-\frac {b n \left (\log (x)-\log \left (a-b n+x y(x)^n\right )\right )}{a-b n}=c_1,y(x)\right ] \]