Internal problem ID [14694]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y=\frac {{\mathrm e}^{t}}{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(t),t$3)-3*diff(y(t),t$2)+3*diff(y(t),t)-y(t)=1/t*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (2 \ln \left (t \right ) t^{2}+\left (4 c_{3} -3\right ) t^{2}+4 t c_{2} +4 c_{1} \right ) {\mathrm e}^{t}}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 39
DSolve[y'''[t]-3*y''[t]+3*y'[t]-y[t]==1/t*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^t \left (2 t^2 \log (t)+(-3+4 c_3) t^2+4 c_2 t+4 c_1\right ) \]