75.17.36 problem 586

Internal problem ID [17085]
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 : 586
Date solved : Tuesday, January 28, 2025 at 09:51:56 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=4 x +3 \sin \left (x \right )+\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-2*diff(y(x),x)=4*x+3*sin(x)+cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 14.159 (sec). Leaf size: 101

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-2*D[y[x],x]==4*x+2*Sin[x]+Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-K[3]} \left (c_1+e^{3 K[3]} c_2+\int _1^{K[3]}-\frac {1}{3} e^{K[1]} (\cos (K[1])+4 K[1]+2 \sin (K[1]))dK[1]+e^{3 K[3]} \int _1^{K[3]}\frac {1}{3} e^{-2 K[2]} (\cos (K[2])+4 K[2]+2 \sin (K[2]))dK[2]\right )dK[3]+c_3 \]