15.14.27 problem 27

Internal problem ID [3199]
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
Date solved : Monday, January 27, 2025 at 07:25:53 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y&=\sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 6182

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: 1.926 (sec). Leaf size: 1124

DSolve[D[y[x],{x,4}]+3*D[y[x],{x,2}]-D[y[x],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 )} \]