63.4.29 problem 24

Internal problem ID [13072]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 04:51:22 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ x \left (t \right ) = -\frac {t^{2}}{2}+c_{1} \ln \left (t \right )+c_{2} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

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

\[ x(t)\to -\frac {t^2}{2}+c_1 \log (t)+c_2 \]