Internal problem ID [3793]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 541.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {2 y y^{\prime } x -y^{2}=x a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(2*x*y(x)*diff(y(x),x) = a*x+y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {a x \ln \left (x \right )+c_{1} x} y \left (x \right ) = -\sqrt {a x \ln \left (x \right )+c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 44
DSolve[2 x y[x] y'[x]==a x +y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {a \log (x)+c_1} y(x)\to \sqrt {x} \sqrt {a \log (x)+c_1} \end{align*}