Internal problem ID [3582]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 326.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 128
dsolve((x-a)*(x-b)*diff(y(x),x)+k*(x+y(x)-a)*(x+y(x)-b)+y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {k \left (\frac {b c_{1} \left (-x +b \right )^{k}}{c_{1} \left (-x +b \right )^{k}+\left (-x +a \right )^{k}}-\frac {x c_{1} \left (-x +b \right )^{k}}{c_{1} \left (-x +b \right )^{k}+\left (-x +a \right )^{k}}+\frac {a \left (-x +a \right )^{k}}{c_{1} \left (-x +b \right )^{k}+\left (-x +a \right )^{k}}-\frac {x \left (-x +a \right )^{k}}{c_{1} \left (-x +b \right )^{k}+\left (-x +a \right )^{k}}\right )}{k +1} \]
✓ Solution by Mathematica
Time used: 60.297 (sec). Leaf size: 99
DSolve[(x-a)(x-b)y'[x]+k(x+y[x]-a)(x+y[x]-b)+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (\frac {k (a+b-2 x)}{k+1}+\sqrt {-\frac {k^2 (a-b)^2}{(k+1)^2}} \tan \left (\frac {(k+1) \sqrt {-\frac {k^2 (a-b)^2}{(k+1)^2}} (\log (x-b)-\log (x-a))}{2 (a-b)}+c_1\right )\right ) \]