65.11.4 problem 18.1 (iv)

Internal problem ID [13793]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 18, The variation of constants formula. Exercises page 168
Problem number : 18.1 (iv)
Date solved : Tuesday, January 28, 2025 at 06:03:39 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} x^{\prime \prime }-2 x&=t^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(t^2*diff(x(t),t$2)-2*x(t)=t^3,x(t), singsol=all)
 

\[ x \left (t \right ) = c_{2} t^{2}+\frac {t^{3}}{4}+\frac {c_{1}}{t} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 25

DSolve[t^2*D[x[t],{t,2}]-2*x[t]==t^3,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {t^3}{4}+c_2 t^2+\frac {c_1}{t} \]