40.11.11 problem 37

Internal problem ID [6745]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 37
Date solved : Monday, January 27, 2025 at 02:27:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 32

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

\[ y = {\mathrm e}^{\left (1+\sqrt {2}\right ) x} c_2 +{\mathrm e}^{-\left (\sqrt {2}-1\right ) x} c_1 -\frac {{\mathrm e}^{x} \cos \left (x \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 56

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

\[ y(x)\to \frac {1}{3} e^{-\sqrt {2} x} \left (-e^{\left (1+\sqrt {2}\right ) x} \cos (x)+3 e^x \left (c_2 e^{2 \sqrt {2} x}+c_1\right )\right ) \]