Internal problem ID [12675]
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 1.8 page 121
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-\frac {y}{2}=4 \,{\mathrm e}^{\frac {t}{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(t),t)=y(t)/2+4*exp(t/2),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\frac {t}{2}} \left (4 t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 19
DSolve[y'[t]==y[t]/2+4*Exp[t/2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{t/2} (4 t+c_1) \]