Internal problem ID [12331]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-a y=b} \] With initial conditions \begin {align*} [y \left (c \right ) = d] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([diff(y(x),x)=a*y(x)+b,y(c) = d],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (d a +b \right ) {\mathrm e}^{-a \left (c -x \right )}-b}{a} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 39
DSolve[{y'[x]==a*y[x]+b,{y[c]==d}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-a c} \left (b \left (e^{a x}-e^{a c}\right )+a d e^{a x}\right )}{a} \]