Internal problem ID [513]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2}+3 y x +y^{2}-y^{\prime } x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 18
dsolve((x^2+3*x*y(x)+y(x)^2)-x^2* diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (\ln \relax (x )+c_{1}+1\right )}{\ln \relax (x )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 25
DSolve[(x^2+3*x*y[x]+y[x]^2)-x^2* y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (-1-\frac {1}{\log (x)+c_1}\right ) \\ y(x)\to -x \\ \end{align*}