4.3 problem Problem 11

Internal problem ID [2158]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (x +y\right )^{2}}{2 x^{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.25 (sec). Leaf size: 17

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

\begin{align*} y(x)\to x \tan \left (\frac {\log (x)}{2}+c_1\right ) \\ \end{align*}