66.2.30 problem Problem 41

Internal problem ID [13929]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 41
Date solved : Tuesday, January 28, 2025 at 06:08:58 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=x \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 48

dsolve(diff(y(x),x$6)-3*diff(y(x),x$5)+3*diff(y(x),x$4)-diff(y(x),x$3)=x,y(x), singsol=all)
 

\[ y = \left (c_{3} x^{2}+\left (c_{2} -6 c_{3} \right ) x +c_{1} -3 c_{2} +12 c_{3} \right ) {\mathrm e}^{x}-\frac {x^{4}}{24}-\frac {x^{3}}{2}+\frac {c_4 \,x^{2}}{2}+x c_5 +c_6 \]

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 61

DSolve[D[y[x],{x,6}]-3*D[y[x],{x,5}]+3*D[y[x],{x,4}]-D[y[x],{x,3}]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^4}{24}-\frac {x^3}{2}+c_6 x^2+c_3 e^x \left (x^2-6 x+12\right )+c_5 x+c_1 e^x+c_2 e^x (x-3)+c_4 \]