75.16.36 problem 509

Internal problem ID [17009]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 509
Date solved : Tuesday, January 28, 2025 at 09:45:27 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+6*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=x*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (\frac {1}{120} x^{5}+c_{1} +c_{2} x +x^{2} c_{3} +c_4 \,x^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 39

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+6*D[y[x],{x,2}]-4*D[y[x],x]+y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{120} e^x \left (x^5+120 c_4 x^3+120 c_3 x^2+120 c_2 x+120 c_1\right ) \]