7.1.2 problem 2

Internal problem ID [2]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 2
Date solved : Friday, February 07, 2025 at 08:11:43 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\left (x -2\right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

dsolve([diff(y(x),x)=(x-2)^2,y(2) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (x -2\right )^{3}}{3}+1 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

DSolve[{D[y[x],x]==(x-2)^2,{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (x^3-6 x^2+12 x-5\right ) \]