Internal problem ID [13432]
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 (b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=10 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=10*sin(2*x),y(x), singsol=all)
\[ y = \frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+\frac {\sin \left (2 x \right )}{8}-\frac {\cos \left (2 x \right )}{4}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.383 (sec). Leaf size: 46
DSolve[y''''[x]-4*y'''[x]==10*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_4 x^2+c_3 x+\frac {1}{64} \left (16 x+8 \sin (2 x)-16 \cos (2 x)+c_1 e^{4 x}\right )+c_2 \]