20.4.3 problem Problem 11

Internal problem ID [3638]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 11
Date solved : Monday, January 27, 2025 at 07:48:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(diff(y(x),x)=(x+y(x))^2/(2*x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 17

DSolve[D[y[x],x]==(x+y[x])^2/(2*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \tan \left (\frac {\log (x)}{2}+c_1\right ) \]