82.33.26 problem Ex. 26

Internal problem ID [18919]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 26
Date solved : Tuesday, January 28, 2025 at 12:37:04 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&={\mathrm e}^{x}+\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*diff(y(x),x)-2*y(x)=exp(x)+cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{2} \cos \left (x \right )+c_3 \sin \left (x \right )+x +c_{1} \right ) {\mathrm e}^{x}+\frac {\cos \left (x \right )}{10}+\frac {3 \sin \left (x \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 40

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*D[y[x],x]-2*y[x]==Exp[x]+Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x+c_3)+\left (\frac {1}{10}+c_2 e^x\right ) \cos (x)+\left (\frac {3}{10}+c_1 e^x\right ) \sin (x) \]