71.11.7 problem 7

Internal problem ID [14516]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:42:53 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y&={\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 5468

dsolve(diff(y(x),x$6)-12*diff(y(x),x$5)+63*diff(y(x),x$4)-18*diff(y(x),x$3)+315*diff(y(x),x$2)-300*diff(y(x),x)+125*y(x)=exp(x)*(48*cos(x)+96*sin(x)),y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 292

DSolve[D[y[x],{x,6}]-12*D[y[x],{x,5}]+63*D[y[x],{x,4}]-18*D[y[x],{x,3}]+315*D[y[x],{x,2}]-300*D[y[x],x]+125*y[x]==Exp[x]*(48*Cos[x]+96*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,4\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,2\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,5\right ]\right )+c_6 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,6\right ]\right )-\frac {48 e^x (352 \sin (x)+1011 \cos (x))}{229205} \]