Internal problem ID [2182]
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 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x \left (y^{\prime }+y^{3} x^{2}\right )+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(2*x*(diff(y(x),x)+y(x)^3*x^2)+y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {x^{3}+x c_{1}}} \\ y \relax (x ) = -\frac {1}{\sqrt {x^{3}+x c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.247 (sec). Leaf size: 40
DSolve[2*x*(y'[x]+y[x]^3*x^2)+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x \left (x^2+c_1\right )}} \\ y(x)\to \frac {1}{\sqrt {x \left (x^2+c_1\right )}} \\ y(x)\to 0 \\ \end{align*}