Internal problem ID [11575]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x +y-y^{3} x^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x*diff(y(x),x)+y(x)=x^3*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {-2 x +c_{1}}\, x} \\ y \left (x \right ) &= -\frac {1}{\sqrt {-2 x +c_{1}}\, x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.6 (sec). Leaf size: 44
DSolve[x*y'[x]+y[x]==x^3*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x^2 (-2 x+c_1)}} \\ y(x)\to \frac {1}{\sqrt {x^2 (-2 x+c_1)}} \\ y(x)\to 0 \\ \end{align*}