63.11.6 problem 1(f)

Internal problem ID [13159]
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 2.4.1 Cauchy-Euler equations. Exercises page 120
Problem number : 1(f)
Date solved : Tuesday, January 28, 2025 at 05:11:27 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0\\ x^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([t^2*diff(x(t),t$2)+3*t*diff(x(t),t)-8*x(t)=0,x(1) = 0, D(x)(1) = 2],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {t^{6}-1}{3 t^{4}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 17

DSolve[{t^2*D[x[t],{t,2}]+3*t*D[x[t],t]-8*x[t]==0,{x[1]==0,Derivative[1][x][1 ]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {t^6-1}{3 t^4} \]