77.1.129 problem 156 (page 236)

Internal problem ID [18019]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 156 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:03 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=\left (1+x \right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 39

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+6*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=(x+1)*exp(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x} \left (x^{5}+5 x^{4}+\left (120 c_4 +4\right ) x^{3}+120 c_{3} x^{2}+120 c_{2} x +120 c_{1} \right )}{120} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 42

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+6*D[y[x],{x,2}]-4*D[y[x],x]+y[x]==(x+1)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\frac {x^5}{120}+\frac {x^4}{24}+c_4 x^3+c_3 x^2+c_2 x+c_1\right ) \]