Internal problem ID [985]
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: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-2 y-x y^{3}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = 2 \sqrt {2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.044 (sec). Leaf size: 13
dsolve([diff(y(x),x)-2*y(x)=x*y(x)^3,y(0) = 2*2^(1/2)],y(x), singsol=all)
\[ y \relax (x ) = \frac {4}{\sqrt {-8 x +2}} \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 34
DSolve[{y'[x]-2*y[x]==x*y[x]^3,y[0]==2*Sqrt[2]},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 i \sqrt {2} e^{2 x}}{\sqrt {e^{4 x} (4 x-1)}} \\ \end{align*}