Internal problem ID [11655]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }+\frac {\left (1+t \right ) x}{2 t}-\frac {1+t}{x t}=0} \]
✓ Solution by Maple
Time used: 0.031 (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 {t \,{\mathrm e}^{-t} c_{1} +2 t^{2}}}{t} \\ x \left (t \right ) &= -\frac {\sqrt {t \,{\mathrm e}^{-t} c_{1} +2 t^{2}}}{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.335 (sec). Leaf size: 78
DSolve[x'[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+2 c_1}}}{\sqrt {t}} \\ x(t)\to \frac {\sqrt {2 t+e^{-t+2 c_1}}}{\sqrt {t}} \\ x(t)\to -\sqrt {2} \\ x(t)\to \sqrt {2} \\ \end{align*}