63.12.8 problem 3

Internal problem ID [13170]
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 : 3
Date solved : Tuesday, January 28, 2025 at 05:11:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x&=4 t^{7} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(t^2*diff(x(t),t$2)-3*t*diff(x(t),t)+3*x(t)=4*t^7,x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (t^{6}+3 c_{1} t^{2}+6 c_{2} \right ) t}{6} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

DSolve[t^2*D[x[t],{t,2}]-3*t*D[x[t],t]+3*x[t]==4*t^7,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {t^7}{6}+c_2 t^3+c_1 t \]