Internal problem ID [5090]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{2 x}-\frac {x^{2}}{2 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 35
dsolve(diff(y(x),x)=y(x)/(2*x)+x^2/(2*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {2 x^{3}+4 c_{1} x}}{2} \\ y \relax (x ) = \frac {\sqrt {2 x^{3}+4 c_{1} x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 56
DSolve[y'[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*}