Internal problem ID [1997]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.24 (d) .
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{2}}{x^{2}}-\frac {1}{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 18
dsolve(diff(y(x),x)-y(x)^2/x^2=1/4,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\ln \relax (x )+c_{1}-2\right )}{2 \ln \relax (x )+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 31
DSolve[y'[x]-y[x]^2/x^2==1/4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\frac {1}{2}-\frac {1}{\log (x)+4 c_1}\right ) \\ y(x)\to \frac {x}{2} \\ \end{align*}