Internal problem ID [14872]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y={\mathrm e}^{t} \ln \left (t \right )} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 37
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+y(t)=exp(t)*ln(t),y(1) = 1, D(y)(1) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{t} \left (2 \ln \left (t \right ) t^{2}-4 \,{\mathrm e}^{-1} t -3 t^{2}+8 \,{\mathrm e}^{-1}+4 t -1\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 39
DSolve[{y''[t]-2*y'[t]+y[t]==Exp[t]*Log[t],{y[1]==1,y'[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{t-1} \left (e \left (-3 t^2+4 t-1\right )+2 e t^2 \log (t)-4 t+8\right ) \]