Internal problem ID [12780]
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.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y={\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right )} \]
✓ 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: 0.024 (sec). Leaf size: 292
DSolve[y''''''[x]-12*y'''''[x]+63*y''''[x]-18*y'''[x]+315*y''[x]-300*y'[x]+125*y[x]==Exp[x]*(48*Cos[x]+96*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,4\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,2\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,5\right ]\right )+c_6 \exp \left (x \text {Root}\left [\text {$\#$1}^6-12 \text {$\#$1}^5+63 \text {$\#$1}^4-18 \text {$\#$1}^3+315 \text {$\#$1}^2-300 \text {$\#$1}+125\&,6\right ]\right )-\frac {48 e^x (352 \sin (x)+1011 \cos (x))}{229205} \]