Internal problem ID [2939]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 191.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x +2 y-a \,x^{2 k} y^{k}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
dsolve(x*diff(y(x),x)+2*y(x) = a*x^(2*k)*y(x)^k,y(x), singsol=all)
\[ y \relax (x ) = 2^{\frac {1}{k -1}} \left (\frac {-x^{2} a k +a \,x^{2}+2 c_{1}}{x^{2}}\right )^{-\frac {1}{k -1}} x^{-\frac {2 k}{k -1}} \]
✓ Solution by Mathematica
Time used: 15.764 (sec). Leaf size: 45
DSolve[x y'[x]+2 y[x]==a x^(2 k)y[x]^k,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {1}{2} a x^{2 k}-\frac {1}{2} a k x^{2 k}+c_1 x^{2 k-2}\right ){}^{\frac {1}{1-k}} \\ \end{align*}