Internal problem ID [983]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-y x -y^{3} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x)-x*y(x)=x^3*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {{\mathrm e}^{-x^{2}} c_{1}-x^{2}+1}} \\ y \relax (x ) = -\frac {1}{\sqrt {{\mathrm e}^{-x^{2}} c_{1}-x^{2}+1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.876 (sec). Leaf size: 80
DSolve[y'[x]-x*y[x]==x^3*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i e^{\frac {x^2}{2}}}{\sqrt {e^{x^2} \left (x^2-1\right )-c_1}} \\ y(x)\to \frac {i e^{\frac {x^2}{2}}}{\sqrt {e^{x^2} \left (x^2-1\right )-c_1}} \\ y(x)\to 0 \\ \end{align*}