40.10.7 problem 16

Internal problem ID [6729]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 15. Linear equations with constant coefficients (Variation of parameters). Supplemetary problems. Page 98
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:25:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

\[ y = -\frac {\cos \left (2 x \right ) {\mathrm e}^{x}}{8}+c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{x} \left (c_1 -\frac {\sin \left (2 x \right )}{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 37

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

\[ y(x)\to c_1 e^x+c_2 e^{-x}-\frac {1}{8} e^x (\sin (2 x)+\cos (2 x)+2) \]