72.7.9 problem 9

Internal problem ID [14750]
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 1.9 page 133
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 07:13:40 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-\frac {y}{t}+2 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 11

dsolve([diff(y(t),t)=-y(t)/t+2,y(1) = 3],y(t), singsol=all)
 

\[ y = t +\frac {2}{t} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 12

DSolve[{D[y[t],t]==-y[t]/t+2,{y[1]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t+\frac {2}{t} \]