48.1.10 problem Example 3.10

Internal problem ID [7511]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.10
Date solved : Monday, January 27, 2025 at 03:03:13 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(diff(y(x),x)=y(x)/(2*x)+x^2/(2*y(x)),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {x \left (x^{2}+2 c_{1} \right )}}{2} \\ y &= \frac {\sqrt {2}\, \sqrt {x \left (x^{2}+2 c_{1} \right )}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 56

DSolve[D[y[x],x]==y[x]/(2*x)+x^2/(2*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {x^2+2 c_1}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {x} \sqrt {x^2+2 c_1}}{\sqrt {2}} \\ \end{align*}