8.1.1 problem 1

Internal problem ID [651]
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 : 1
Date solved : Monday, January 27, 2025 at 02:56:43 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 x +1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

dsolve([diff(y(x),x) = 1+2*x,y(0) = 3],y(x), singsol=all)
 

\[ y = x^{2}+x +3 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 11

DSolve[{D[y[x],x]==1+2*x,y[0]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+x+3 \]