Internal problem ID [4681]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number: Problem 12.6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N-t \ln \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(t^2*diff(N(t),t$2)-2*t*diff(N(t),t)+2*N(t)=t*ln(t),N(t), singsol=all)
\[ N \relax (t ) = t^{2} c_{2}+t c_{1}-\frac {t \left (\ln \relax (t )^{2}+2 \ln \relax (t )+2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 27
DSolve[t^2*n''[t]-2*t*n'[t]+2*n[t]==t*Log[t],n[t],t,IncludeSingularSolutions -> True]
\begin{align*} n(t)\to -\frac {1}{2} t \log (t) (\log (t)+2)+t (c_2 t-1+c_1) \\ \end{align*}