77.1.130 problem 157 (page 236)

Internal problem ID [18020]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 157 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

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

\[ y = \frac {\left (-x^{2}+8 c_{1} \right ) \cos \left (2 x \right )}{8}+\frac {\sin \left (2 x \right ) \left (x +16 c_{2} \right )}{16} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{64} \left (\left (-8 x^2+1+64 c_1\right ) \cos (2 x)+4 (x+16 c_2) \sin (2 x)\right ) \]