69.1.110 problem 157

Internal problem ID [14263]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 157
Date solved : Tuesday, January 28, 2025 at 06:24:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 62

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

\[ y(x)\to \sin (2 x) \int _1^x\frac {1}{2} \sin (4 K[2])dK[2]+\cos (2 x) \int _1^x-\sin ^2(2 K[1])dK[1]+c_1 \cos (2 x)+c_2 \sin (2 x) \]