69.1.103 problem 150

Internal problem ID [14256]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 150
Date solved : Tuesday, January 28, 2025 at 06:23:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

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

\[ y = \left (\frac {2 \left (-\cos \left (2 x \right )-3 \sin \left (2 x \right )\right ) {\mathrm e}^{2 x}}{5}+{\mathrm e}^{3 x} c_{1} +c_{2} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 35

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

\[ y(x)\to c_1 e^{-2 x}+c_2 e^x-\frac {2}{5} (3 \sin (2 x)+\cos (2 x)) \]