Internal problem ID [3285]
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]
Solve \begin {gather*} \boxed {2 y^{\prime } y x -a x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (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 \relax (x ) = \sqrt {a x \ln \relax (x )+c_{1} x} \\ y \relax (x ) = -\sqrt {a x \ln \relax (x )+c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.261 (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*}