29.7.17 problem 192

Internal problem ID [4792]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 192
Date solved : Monday, January 27, 2025 at 09:38:10 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=4 y-4 \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x*diff(y(x),x) = 4*y(x)-4*sqrt(y(x)),y(x), singsol=all)
 

\[ -c_{1} x^{2}+\sqrt {y \left (x \right )}-1 = 0 \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 31

DSolve[x D[y[x],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*}