Internal problem ID [2228]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 27.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y=\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 1673
dsolve(diff(y(x),x$4)+3*diff(y(x),x$2)-diff(y(x),x)+2*y(x)=sin(2*x),y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 1.487 (sec). Leaf size: 1124
DSolve[y''''[x]+3*y''[x]-y'[x]+2*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x \text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]} c_1+e^{x \text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]} c_2+e^{x \text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]} c_3+e^{x \text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]} c_4-\frac {\left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (2 \cos (2 x)+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ] \sin (2 x)\right )}{\sqrt {761} \left (4+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]^2\right )}+\frac {\left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (2 \cos (2 x)+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ] \sin (2 x)\right )}{\sqrt {761} \left (4+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]^2\right )}-\frac {\left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]\right ) \left (2 \cos (2 x)+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ] \sin (2 x)\right )}{\sqrt {761} \left (4+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]^2\right )}-\frac {e^{\left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) x+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,1\right ] x} \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]-\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (\left (\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \sin (2 x)-2 \cos (2 x)\right )}{\sqrt {761} \left (-2 i+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right ) \left (2 i+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,2\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,3\right ]+\text {Root}\left [\text {$\#$1}^4+3 \text {$\#$1}^2-\text {$\#$1}+2\&,4\right ]\right )} \]