Internal problem ID [12348]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page
368
Problem number: Problem 13(d).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y=-t^{2}+2 t -10} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.391 (sec). Leaf size: 38
dsolve([diff(y(t),t$3)-5*diff(y(t),t$2)+diff(y(t),t)-y(t)=2*t-10-t^2,y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\munderset {\underline {\hspace {1.25 ex}}\alpha =\operatorname {RootOf}\left (\textit {\_Z}^{3}-5 \textit {\_Z}^{2}+\textit {\_Z} -1\right )}{\sum }\left (\underline {\hspace {1.25 ex}}\alpha -4\right ) \left (\underline {\hspace {1.25 ex}}\alpha -7\right ) {\mathrm e}^{\underline {\hspace {1.25 ex}}\alpha t}\right )}{26}+t^{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 1009
DSolve[{y'''[t]-5*y''[t]+y'[t]-y[t]==2*t-10-t^2,{y[0]==2,y'[0]==0,y''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {-\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ] \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]^2 t^2+\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ] \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]^2 t^2+\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]^2 \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ] t^2-\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]^2 \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ] t^2-\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ] \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]^2 t^2+\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]^2 \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ] t^2-2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ] \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]^2+2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ] \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]^2+2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]-2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]+2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]^2 \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]-2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]^2 \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]-2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ] \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]^2-2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]+2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]+2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]^2 \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]+2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]-2 e^{t \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]} \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]}{\left (\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]-\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]\right ) \left (-\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]+\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]\right ) \left (-\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]+\text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]\right )} \]