8.1.2 problem 2

Internal problem ID [652]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:56:44 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: 0.006 (sec). Leaf size: 13

dsolve([diff(y(x),x) = (-2+x)^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]==(-2+x)^2,y[2]==1},y[x],x,IncludeSingularSolutions -> True]
 

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