Internal problem ID [15269]
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. Trial and error method. Exercises page 132
Problem number: 499.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }={\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+diff(y(x),x$2)=exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} \left (x +2\right )+c_{2} \right ) {\mathrm e}^{-x}+c_{3} x +c_{4} +\frac {{\mathrm e}^{4 x}}{400} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 36
DSolve[y''''[x]+2*y'''[x]+y''[x]==Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{4 x}}{400}+e^{-x} (c_2 (x+2)+c_1)+c_4 x+c_3 \]