36.1.18 problem 18

Internal problem ID [6273]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 18
Date solved : Monday, January 27, 2025 at 01:52:42 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x^{3} \left (1-y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

dsolve([diff(y(x),x)=x^3*(1-y(x)),y(0) = 3],y(x), singsol=all)
 

\[ y = 1+2 \,{\mathrm e}^{-\frac {x^{4}}{4}} \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 18

DSolve[{D[y[x],x]==x^3*(1-y[x]),{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
 

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