75.16.69 problem 542

Internal problem ID [17042]
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 : 542
Date solved : Tuesday, January 28, 2025 at 09:47:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

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

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{x}+x^{3}+6 x^{2}+18 x +24 \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 31

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

\[ y(x)\to x^3+6 x^2+x \left (18+c_2 e^x\right )+c_1 e^x+24 \]