72.1.10 problem 13

Internal problem ID [14610]
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 : 13
Date solved : Tuesday, January 28, 2025 at 06:44:27 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {\ln \left (t^{2}+1\right )+c_{1}} \\ y &= -\sqrt {\ln \left (t^{2}+1\right )+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 41

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

\begin{align*} y(t)\to -\sqrt {\log \left (t^2+1\right )+2 c_1} \\ y(t)\to \sqrt {\log \left (t^2+1\right )+2 c_1} \\ \end{align*}