75.16.63 problem 536

Internal problem ID [17036]
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 : 536
Date solved : Tuesday, January 28, 2025 at 09:47:15 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

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

\[ y = -\frac {c_{1} {\mathrm e}^{-2 x}}{2}+\frac {\left (-1-5 x \right ) \cos \left (x \right )}{50}+\frac {\left (-5 x +14\right ) \sin \left (x \right )}{100}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.384 (sec). Leaf size: 48

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

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