Internal problem ID [12907]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-2 y=-t} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([diff(y(t),t)=2*y(t)-t,y(0) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t}{2}+\frac {1}{4}+\frac {{\mathrm e}^{2 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 19
DSolve[{y'[t]==2*y[t]-t,{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} \left (2 t+e^{2 t}+1\right ) \]