75.16.55 problem 528

Internal problem ID [17028]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 528
Date solved : Tuesday, January 28, 2025 at 09:46:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-2 y&=8 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)+4*diff(y(x),x)-2*y(x)=8*sin(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\left (-2+\sqrt {6}\right ) x} c_{2} +{\mathrm e}^{-\left (2+\sqrt {6}\right ) x} c_{1} -\frac {16 \cos \left (2 x \right )}{25}-\frac {12 \sin \left (2 x \right )}{25} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 52

DSolve[D[y[x],{x,2}]+4*D[y[x],x]-2*y[x]==8*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-\left (\left (2+\sqrt {6}\right ) x\right )}+c_2 e^{\left (\sqrt {6}-2\right ) x}-\frac {4}{25} (3 \sin (2 x)+4 \cos (2 x)) \]