Internal problem ID [12686]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-4 y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x)=4*y(x)+1,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{4}+\frac {5 \,{\mathrm e}^{4 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 18
DSolve[{y'[x]==4*y[x]+1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (5 e^{4 x}-1\right ) \]