39.3.6 problem Problem 12.6

Internal problem ID [6532]
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
Date solved : Monday, January 27, 2025 at 02:11:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N&=t \ln \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(t^2*diff(N(t),t$2)-2*t*diff(N(t),t)+2*N(t)=t*ln(t),N(t), singsol=all)
 

\[ N = -\frac {t \left (\ln \left (t \right )^{2}-2 c_1 t +2 \ln \left (t \right )-2 c_2 +2\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 30

DSolve[t^2*D[ n[t],{t,2}]-2*t*D[ n[t],t]+2*n[t]==t*Log[t],n[t],t,IncludeSingularSolutions -> True]
 

\[ n(t)\to -\frac {1}{2} t \log ^2(t)-t \log (t)+t (c_2 t-1+c_1) \]