75.17.5 problem 555

Internal problem ID [17054]
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 : 555
Date solved : Tuesday, January 28, 2025 at 09:47:53 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&={\mathrm e}^{x}+1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-diff(y(x),x$2)=1+exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.547 (sec). Leaf size: 69

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]==1+Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \int _1^x\int _1^{K[2]}\left (e^{K[1]} (c_1+K[1])-1\right )dK[1]dK[2]+c_3 x+c_2 \\ y(x)\to -\frac {x^2}{2}+x+e^x (x-2)+c_3 x+e-\frac {1}{2}+c_2 \\ \end{align*}