71.4.15 problem 15

Internal problem ID [14387]
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 : 15
Date solved : Tuesday, January 28, 2025 at 06:29:18 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=a y+b \end{align*}

With initial conditions

\begin{align*} y \left (c \right )&=d \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 27

dsolve([diff(y(x),x)=a*y(x)+b,y(c) = d],y(x), singsol=all)
 

\[ y = \frac {\left (a d +b \right ) {\mathrm e}^{-a \left (-x +c \right )}-b}{a} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 39

DSolve[{D[y[x],x]==a*y[x]+b,{y[c]==d}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-a c} \left (b \left (e^{a x}-e^{a c}\right )+a d e^{a x}\right )}{a} \]