2.30 problem 31

Internal problem ID [508]

Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section: Section 2.2. Page 48
Problem number: 31.
ODE order: 1.
ODE degree: 1.

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

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

Solution by Maple

Time used: 0.008 (sec). Leaf size: 11

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

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

Solution by Mathematica

Time used: 0.19 (sec). Leaf size: 13

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

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