64.5.5 problem 5

Internal problem ID [13318]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:22:02 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(diff(x(t),t)+x(t)/t^2=1/t^2,x(t), singsol=all)
 

\[ x \left (t \right ) = 1+{\mathrm e}^{\frac {1}{t}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 20

DSolve[D[x[t],t]+x[t]/t^2==1/t^2,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 1+c_1 e^{\frac {1}{t}} \\ x(t)\to 1 \\ \end{align*}