Internal problem ID [13434]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.12 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=32 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=32*x,y(x), singsol=all)
\[ y = -\frac {x^{4}}{3}-\frac {x^{3}}{3}+\frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 43
DSolve[y''''[x]-4*y'''[x]==32*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^4}{3}-\frac {x^3}{3}+c_4 x^2+c_3 x+\frac {1}{64} c_1 e^{4 x}+c_2 \]