Internal problem ID [12775]
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: 2.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime }=24 x^{2}-6 x +14+32 \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(x),x$4)+4*diff(y(x),x$2)=24*x^2-6*x+14+32*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-c_{1} -10\right ) \cos \left (2 x \right )}{4}+\frac {\left (-8 x -c_{2} \right ) \sin \left (2 x \right )}{4}+\frac {x^{4}}{2}-\frac {x^{3}}{4}+\frac {x^{2}}{4}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 1.052 (sec). Leaf size: 54
DSolve[y''''[x]+4*y''[x]==24*x^2-6*x+14+32*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (2 x^4-x^3+x^2+4 c_4 x-(12+c_1) \cos (2 x)-(8 x+c_2) \sin (2 x)+4 c_3\right ) \]