62.27.7 problem Ex 7

Internal problem ID [12945]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
Problem number : Ex 7
Date solved : Tuesday, January 28, 2025 at 04:44:46 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&={\mathrm e}^{x}+4 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 38

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

\[ y = 4+\left (c_4 x +c_{2} \right ) {\mathrm e}^{-x}+\frac {\left (3+2 x^{2}+4 \left (-1+4 c_3 \right ) x +16 c_{1} \right ) {\mathrm e}^{x}}{16} \]

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 124

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

\[ y(x)\to \frac {1}{8} e^{-x} \left (8 \int _1^x-\frac {1}{4} e^{K[1]} \left (4+e^{K[1]}\right ) (K[1]-1)dK[1]+8 e^{2 x} \int _1^x-\frac {1}{4} e^{-K[2]} \left (4+e^{K[2]}\right ) (K[2]+1)dK[2]+2 e^{2 x} x^2+e^{2 x} x+16 x+8 c_2 x+8 c_4 e^{2 x} x+8 c_3 e^{2 x}+8 c_1\right ) \]