71.4.13 problem 13

Internal problem ID [14385]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 06:29:14 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=4 y-5 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([diff(y(x),x)=4*y(x)-5,y(1) = 4],y(x), singsol=all)
 

\[ y = \frac {5}{4}+\frac {11 \,{\mathrm e}^{4 x -4}}{4} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 20

DSolve[{D[y[x],x]==4*y[x]-5,{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {11}{4} e^{4 x-4}+\frac {5}{4} \]