71.5.1 problem 1

Internal problem ID [14397]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:29:43 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 x +1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

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

\[ y = \frac {3}{2} x^{2}+x -\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 17

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

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