29.10.9 problem 275

Internal problem ID [4875]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 275
Date solved : Monday, January 27, 2025 at 09:45:56 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }+y x +\sqrt {y}&=0 \end{align*}

✓ 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)
 

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

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 21

DSolve[x^2 D[y[x],x]+x y[x]+Sqrt[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (1+c_1 \sqrt {x}\right ){}^2}{x^2} \]