7.7 problem 182

Internal problem ID [2930]

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]

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

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)
 

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

Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 32

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

\begin{align*} y(x)\to \frac {1}{-\frac {b x^n}{a-n}+c_1 x^a} \\ y(x)\to 0 \\ \end{align*}