Internal problem ID [11642]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }+\frac {x}{t^{2}}=\frac {1}{t^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.029 (sec). Leaf size: 20
DSolve[x'[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*}