29.25.22 problem 719

Internal problem ID [5309]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 719
Date solved : Monday, January 27, 2025 at 11:08:18 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (a +x y^{n}\right ) y^{\prime }+b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.336 (sec). Leaf size: 38

dsolve(x*(a+x*y(x)^n)*diff(y(x),x)+b*y(x) = 0,y(x), singsol=all)
 

\[ \left (x y \left (x \right )^{n}-b n +a \right )^{b n} \left (y \left (x \right )^{n}\right )^{-a} x^{-b n}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.285 (sec). Leaf size: 61

DSolve[x(a+x y[x]^n)D[y[x],x]+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {a n \log (a y(x)-b n y(x))}{a-b n}-\frac {b n \left (\log (x)-\log \left (a-b n+x y(x)^n\right )\right )}{a-b n}=c_1,y(x)\right ] \]