Internal problem ID [15337]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 568.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }={\mathrm e}^{x}+3 \sin \left (2 x \right )+1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)=exp(x)+3*sin(2*x)+1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-\frac {18 \sin \left (x \right )^{2}}{5}+\frac {9 \sin \left (x \right ) \cos \left (x \right )}{5}+x^{3}+\left (12 c_{2} -\frac {18}{5}\right ) x^{2}+\left (24 c_{3} -\frac {9}{5}\right ) x +24 c_{4} \right ) {\mathrm e}^{4 x}+\frac {24 \,{\mathrm e}^{5 x}}{5}-\frac {3 c_{1}}{8}\right ) {\mathrm e}^{-4 x}}{24} \]
✓ Solution by Mathematica
Time used: 0.877 (sec). Leaf size: 59
DSolve[y''''[x]+4*y'''[x]==Exp[x]+3*Sin[2*x]+1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{24}+c_4 x^2+\frac {e^x}{5}+\frac {3}{80} \sin (2 x)+\frac {3}{40} \cos (2 x)+c_3 x-\frac {1}{64} c_1 e^{-4 x}+c_2 \]