79.1.26 problem 6

Internal problem ID [18513]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 11:51:37 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} t^{2} x^{\prime \prime }-6 x^{\prime } t +12 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(t^2*diff(x(t),t$2)-6*t*diff(x(t),t)+12*x(t)=0,x(t), singsol=all)
 

\[ x = t^{3} \left (c_{2} t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

DSolve[t^2*D[x[t],{t,2}]-6*t*D[x[t],t]+12*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t^3 (c_2 t+c_1) \]