Internal problem ID [5136]
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 3.6 Summary and Problems. Page
218
Problem number: Problem 3.22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-1/x^(1/2)*diff(y(x),x)+1/(4*x^2)*(x+x^(1/2)-8)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{\sqrt {x}}}{x}+c_{2} {\mathrm e}^{\sqrt {x}} x^{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 30
DSolve[y''[x]-1/x^(1/2)*y'[x]+1/(4*x^2)*(x+x^(1/2)-8)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\sqrt {x}} \left (c_2 x^3+3 c_1\right )}{3 x} \\ \end{align*}