63.12.4 problem 1(d)

Internal problem ID [13166]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.4.2 Variation of parameters. Exercises page 124
Problem number : 1(d)
Date solved : Tuesday, January 28, 2025 at 05:11:42 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: 0.002 (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]
 

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