Internal problem ID [2940]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 192.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -4 y+4 \sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(x*diff(y(x),x) = 4*y(x)-4*sqrt(y(x)),y(x), singsol=all)
\[ -c_{1} x^{2}+\sqrt {y \relax (x )}-1 = 0 \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 31
DSolve[x y'[x]==4(y[x]-Sqrt[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (1+e^{\frac {c_1}{2}} x^2\right ){}^2 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}