Internal problem ID [2932]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 184.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -2 x +y-a \,x^{n} \left (x -y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(x*diff(y(x),x) = 2*x-y(x)+a*x^n*(x-y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \,x^{n} a +c_{1} x^{2}-n +1}{a \,x^{n}+c_{1} x} \]
✓ Solution by Mathematica
Time used: 0.912 (sec). Leaf size: 164
DSolve[x y'[x]==2 x -y[x]+a x^n(x-y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^{-n} \left (2 a x^{n+\sqrt {(n-1)^2}+1}+2 a c_1 \sqrt {(n-1)^2} x^{n+1}-\left (n+\sqrt {(n-1)^2}-1\right ) x^{\sqrt {(n-1)^2}}-c_1 \left (-n+\sqrt {(n-1)^2}+1\right ) (n-1)\right )}{2 a \left (x^{\sqrt {(n-1)^2}}+c_1 \sqrt {(n-1)^2}\right )} \\ y(x)\to \frac {x^{-n} \left (2 a x^{n+1}-n+\sqrt {(n-1)^2}+1\right )}{2 a} \\ \end{align*}