71.7.1 problem 1

Internal problem ID [14422]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:30:31 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y+1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 12

dsolve([diff(y(x),x)=4*y(x)+1,y(0) = 1],y(x), singsol=all)
 

\[ y = -\frac {1}{4}+\frac {5 \,{\mathrm e}^{4 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 18

DSolve[{D[y[x],x]==4*y[x]+1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (5 e^{4 x}-1\right ) \]