29.7.7 problem 182

Internal problem ID [4782]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 182
Date solved : Monday, January 27, 2025 at 09:37:39 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.289 (sec). Leaf size: 36

DSolve[x D[y[x],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*}