82.33.25 problem Ex. 25

Internal problem ID [18918]
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. 25
Date solved : Tuesday, January 28, 2025 at 12:37:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

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

\[ y \left (x \right ) = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{x} c_{1} -\frac {{\mathrm e}^{x} \cos \left (2 x \right )}{8}-\frac {\cos \left (3 x \right )}{30}-\frac {{\mathrm e}^{x} \sin \left (2 x \right )}{8}-\frac {\sin \left (3 x \right )}{15} \]

✓ Solution by Mathematica

Time used: 0.190 (sec). Leaf size: 55

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

\[ y(x)\to c_1 e^x+c_2 e^{3 x}+\frac {1}{120} \left (-15 e^x \sin (2 x)-8 \sin (3 x)-15 e^x \cos (2 x)-4 \cos (3 x)\right ) \]