75.17.37 problem 587

Internal problem ID [17086]
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 : 587
Date solved : Tuesday, January 28, 2025 at 09:51:56 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 44

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

\[ y = \frac {\left (8 x^{2}+64 c_{2} -12 x +7\right ) {\mathrm e}^{2 x}}{128}-\frac {x^{3}}{12}-\frac {c_{1} {\mathrm e}^{-2 x}}{2}-\frac {x}{8}+c_{3} +\frac {\cos \left (x \right )}{5} \]

✓ Solution by Mathematica

Time used: 17.302 (sec). Leaf size: 109

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

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