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]
\[ \boxed {y^{\prime }-\frac {\left (x +y\right )^{2}}{2 x^{2}}=0} \]
✓ 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)
\[ y \left (x \right ) = \tan \left (\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.203 (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*}