75.17.34 problem 584

Internal problem ID [17083]
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. Superposition principle. Exercises page 137
Problem number : 584
Date solved : Tuesday, January 28, 2025 at 09:51:51 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

\[ y = \frac {\left (x^{2}+\left (2 c_{1} -2\right ) x -2 c_{1} +2 c_{2} +2\right ) {\mathrm e}^{x}}{2}+x^{2}+4 x +c_{3} \]

✓ Solution by Mathematica

Time used: 21.490 (sec). Leaf size: 74

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

\[ y(x)\to \int _1^xe^{K[3]} \left (c_1+c_2 K[3]+\int _1^{K[3]}K[1] \left (-2 e^{-K[1]} K[1]-1\right )dK[1]+K[3] \int _1^{K[3]}\left (2 e^{-K[2]} K[2]+1\right )dK[2]\right )dK[3]+c_3 \]