Internal problem ID [3023]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 275.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+y x +\sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x)+x*y(x)+sqrt(y(x)) = 0,y(x), singsol=all)
\[ \sqrt {y \relax (x )}-\frac {1}{x}-\frac {c_{1}}{\sqrt {x}} = 0 \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 21
DSolve[x^2 y'[x]+x y[x]+Sqrt[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (1+c_1 \sqrt {x}\right ){}^2}{x^2} \\ \end{align*}