Internal problem ID [3069]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 321.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _Riccati]
Solve \begin {gather*} \boxed {\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.077 (sec). Leaf size: 39
dsolve((x-a)^2*diff(y(x),x)+k*(x+y(x)-a)^2+y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-x +a \right ) \left (c_{1} k \left (-x +a \right )-1\right )}{c_{1} k \left (-x +a \right )+c_{1} \left (-x +a \right )-1} \]
✓ Solution by Mathematica
Time used: 0.219 (sec). Leaf size: 50
DSolve[(x-a)^2 y'[x]+k(x+y[x]-a)^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {k (a-x)}{k+1}+\frac {1}{\frac {k+1}{a-x}+c_1} \\ y(x)\to \frac {k (a-x)}{k+1} \\ \end{align*}