72.6.6 problem 6

Internal problem ID [14731]
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
Date solved : Tuesday, January 28, 2025 at 07:13:02 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=\frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(y(t),t)=y(t)/2+4*exp(t/2),y(t), singsol=all)
 

\[ y = \left (4 t +c_{1} \right ) {\mathrm e}^{\frac {t}{2}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 19

DSolve[D[y[t],t]==y[t]/2+4*Exp[t/2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/2} (4 t+c_1) \]