75.16.26 problem 499

Internal problem ID [16999]
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 : 499
Date solved : Tuesday, January 28, 2025 at 09:45:22 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

\[ y = \left (c_{1} \left (x +2\right )+c_{2} \right ) {\mathrm e}^{-x}+c_{3} x +c_4 +\frac {{\mathrm e}^{4 x}}{400} \]

✓ Solution by Mathematica

Time used: 60.095 (sec). Leaf size: 76

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

\[ y(x)\to \int _1^x\int _1^{K[3]}\frac {1}{5} e^{-K[2]} \left (5 c_1+\left (5 c_2+e^{5 K[2]}\right ) K[2]+5 \int _1^{K[2]}-e^{5 K[1]} K[1]dK[1]\right )dK[2]dK[3]+c_4 x+c_3 \]