Internal problem ID [812]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number: 1.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y-t=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 227
dsolve(diff(y(t),t$4)+4*diff(y(t),t$3)+3*y(t)=t,y(t), singsol=all)
\[ y \relax (t ) = \frac {t}{3}+{\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{\frac {\left (\sqrt {2}\, \left (4+2 \sqrt {2}\right )^{\frac {2}{3}}-2 \left (4+2 \sqrt {2}\right )^{\frac {2}{3}}-2 \left (4+2 \sqrt {2}\right )^{\frac {1}{3}}-2\right ) t}{2}}+c_{3} {\mathrm e}^{-\frac {\left (\sqrt {2}\, \left (4+2 \sqrt {2}\right )^{\frac {2}{3}}-2 \left (4+2 \sqrt {2}\right )^{\frac {2}{3}}-2 \left (4+2 \sqrt {2}\right )^{\frac {1}{3}}+4\right ) t}{4}} \cos \left (\frac {\sqrt {3}\, \left (4+2 \sqrt {2}\right )^{\frac {1}{3}} \left (\left (4+2 \sqrt {2}\right )^{\frac {1}{3}} \sqrt {2}-2 \left (4+2 \sqrt {2}\right )^{\frac {1}{3}}+2\right ) t}{4}\right )+c_{4} {\mathrm e}^{-\frac {\left (\sqrt {2}\, \left (4+2 \sqrt {2}\right )^{\frac {2}{3}}-2 \left (4+2 \sqrt {2}\right )^{\frac {2}{3}}-2 \left (4+2 \sqrt {2}\right )^{\frac {1}{3}}+4\right ) t}{4}} \sin \left (\frac {\sqrt {3}\, \left (4+2 \sqrt {2}\right )^{\frac {1}{3}} \left (\left (4+2 \sqrt {2}\right )^{\frac {1}{3}} \sqrt {2}-2 \left (4+2 \sqrt {2}\right )^{\frac {1}{3}}+2\right ) t}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 90
DSolve[y''''[t]+4*y'''[t]+3*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-t} \left (3 c_2 \exp \left (t \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}+8\&,2\right ]\right )+3 c_3 \exp \left (t \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}+8\&,3\right ]\right )+3 c_1 \exp \left (t \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}+8\&,1\right ]\right )+e^t t+3 c_4\right ) \\ \end{align*}