Internal problem ID [1996]
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 (c) .
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*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 17
dsolve([diff(y(x),x)-y(x)^2/x^2=1/4,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (\ln \relax (x )-4\right )}{2 \ln \relax (x )-4} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 20
DSolve[{y'[x]-y[x]^2/x^2==1/4,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (\log (x)-4)}{2 (\log (x)-2)} \\ \end{align*}