Internal problem ID [6669]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS.
Page 297
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y=1+{\mathrm e}^{t} t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t)-y(t)=1+t*exp(t),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{t} t^{2}}{2}-1+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 19
DSolve[{y'[t]-y[t]==1+t*Exp[t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^t \left (t^2+2\right )-1 \]