64.5.18 problem 18

Internal problem ID [13331]
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 : 18
Date solved : Tuesday, January 28, 2025 at 05:22:35 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 46

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

\begin{align*} x \left (t \right ) &= \frac {\sqrt {c_{1} {\mathrm e}^{-t} t +2 t^{2}}}{t} \\ x \left (t \right ) &= -\frac {\sqrt {c_{1} {\mathrm e}^{-t} t +2 t^{2}}}{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.370 (sec). Leaf size: 80

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

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