72.1.13 problem 16

Internal problem ID [14613]
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 1.2. page 33
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 06:44:34 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 22

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

\begin{align*} y(t)\to -\frac {1}{2}+c_1 t^2 \\ y(t)\to -\frac {1}{2} \\ \end{align*}