75.17.33 problem 583

Internal problem ID [17082]
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. Superposition principle. Exercises page 137
Problem number : 583
Date solved : Tuesday, January 28, 2025 at 09:51:47 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+1&=3 \sin \left (2 x \right )+\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+1=3*sin(2*x)+cos(x),y(x), singsol=all)
 

\[ y = -\frac {c_{1} {\mathrm e}^{-2 x}}{2}+\frac {2 \sin \left (x \right )}{5}-\frac {3 \sin \left (2 x \right )}{8}-\frac {\cos \left (x \right )}{5}-\frac {3 \cos \left (2 x \right )}{8}-\frac {x}{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.491 (sec). Leaf size: 52

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+1==3*Sin[2*x]+Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-2 K[2]} \left (c_1+\int _1^{K[2]}e^{2 K[1]} (\cos (K[1])+3 \sin (2 K[1])-1)dK[1]\right )dK[2]+c_2 \]