18.1.21 problem Problem 14.24 (d)

Internal problem ID [3477]
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)
Date solved : Monday, January 27, 2025 at 07:38:27 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x)-y(x)^2/x^2=1/4,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x \left (\ln \left (x \right )+c_{1} -2\right )}{2 \ln \left (x \right )+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 36

DSolve[D[y[x],x]-y[x]^2/x^2==1/4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x (\log (x)-2+4 c_1)}{2 (\log (x)+4 c_1)} \\ y(x)\to \frac {x}{2} \\ \end{align*}