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]
\[ \boxed {2 x y y^{\prime }-y^{2}=a x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
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 {\left (a \ln \left (x \right )+c_{1} \right ) x} \\ y \left (x \right ) &= -\sqrt {\left (a \ln \left (x \right )+c_{1} \right ) 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*}