75.17.18 problem 568

Internal problem ID [17067]
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 : 568
Date solved : Tuesday, January 28, 2025 at 09:48:55 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 60

dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)=exp(x)+3*sin(2*x)+1,y(x), singsol=all)
 

\[ y = \frac {\left (\left (-\frac {18 \sin \left (x \right )^{2}}{5}+\frac {9 \cos \left (x \right ) \sin \left (x \right )}{5}+x^{3}+\left (12 c_{2} -\frac {18}{5}\right ) x^{2}+\left (24 c_{3} -\frac {9}{5}\right ) x +24 c_4 \right ) {\mathrm e}^{4 x}+\frac {24 \,{\mathrm e}^{5 x}}{5}-\frac {3 c_{1}}{8}\right ) {\mathrm e}^{-4 x}}{24} \]

✓ Solution by Mathematica

Time used: 31.951 (sec). Leaf size: 78

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,3}]==Exp[x]+3*Sin[2*x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}e^{-4 K[2]} \left (c_1+\int _1^{K[2]}e^{4 K[1]} \left (3 \sin (2 K[1])+e^{K[1]}+1\right )dK[1]\right )dK[2]dK[3]dK[4]+x (c_4 x+c_3)+c_2 \]