7.11.22 problem 22

Internal problem ID [343]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:46:02 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime }&={\mathrm e}^{x}+2 x^{2}-5 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 44

dsolve(diff(y(x),x$5)-diff(y(x),x$3)=exp(x)+2*x^2-5,y(x), singsol=all)
 

\[ y = -{\mathrm e}^{-x} c_1 +\frac {\left (-7+2 x +4 c_2 \right ) {\mathrm e}^{x}}{4}-\frac {x^{5}}{30}+\frac {x^{3}}{6}+\frac {c_3 \,x^{2}}{2}+c_4 x +c_5 \]

✓ Solution by Mathematica

Time used: 0.452 (sec). Leaf size: 56

DSolve[D[y[x],{x,5}]-D[y[x],{x,3}]==Exp[x]+2*x^2-5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^5}{30}+\frac {x^3}{6}+c_5 x^2+c_4 x+e^x \left (\frac {x}{2}-\frac {7}{4}+c_1\right )-c_2 e^{-x}+c_3 \]