Internal problem ID [15311]
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: 541.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+2*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 c_{4} x +x^{2}+4 c_{2} \right ) {\mathrm e}^{x}}{4}+\cos \left (x \right ) c_{1} +c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 40
DSolve[y''''[x]-2*y'''[x]+2*y''[x]-2*y'[x]+y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^x \left (x^2-2 x+4 c_4 x+1+4 c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]