75.16.53 problem 526

Internal problem ID [17026]
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 : 526
Date solved : Tuesday, January 28, 2025 at 09:45:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=1+x \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 32

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

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