72.7.7 problem 7

Internal problem ID [14748]
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 : 7
Date solved : Tuesday, January 28, 2025 at 07:13:36 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-\frac {y}{1+t}+2 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 18

dsolve([diff(y(t),t)=-y(t)/(1+t)+2,y(0) = 3],y(t), singsol=all)
 

\[ y = \frac {t^{2}+2 t +3}{t +1} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 19

DSolve[{D[y[t],t]==-y[t]/(1+t)+2,{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^2+2 t+3}{t+1} \]