72.8.13 problem 26

Internal problem ID [14777]
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. Review Exercises for chapter 1. page 136
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 07:15:03 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(diff(y(t),t)= t+2*y(t)/(1+t),y(t), singsol=all)
 

\[ y = \left (t +1\right ) \left (\left (t +1\right ) \ln \left (t +1\right )+c_{1} t +c_{1} +1\right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 26

DSolve[D[y[t],t]==t+2*y[t]/(1+t),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to (t+1)^2 \left (-\frac {t}{t+1}+\log (t+1)+c_1\right ) \]