12.5.11 problem 7

Internal problem ID [1635]
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
Date solved : Monday, January 27, 2025 at 05:15:20 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }-2 y&=x y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \sqrt {2} \end{align*}

✓ Solution by Maple

Time used: 0.026 (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)
 

\[ y = \frac {4}{\sqrt {-8 x +2}} \]

✓ Solution by Mathematica

Time used: 1.839 (sec). Leaf size: 34

DSolve[{D[y[x],x]-2*y[x]==x*y[x]^3,y[0]==2*Sqrt[2]},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 i \sqrt {2} e^{2 x}}{\sqrt {e^{4 x} (4 x-1)}} \]