12.20.5 problem section 9.4, problem 16

Internal problem ID [2226]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number : section 9.4, problem 16
Date solved : Monday, January 27, 2025 at 05:43:48 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y&=x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 30

dsolve(x^4*diff(y(x),x$4)-4*x^3*diff(y(x),x$3)+12*x^2*diff(y(x),x$2)-24*x*diff(y(x),x)+24*y(x)=x^4,y(x), singsol=all)
 

\[ y = x \left (\frac {x^{3} \ln \left (x \right )}{6}+\left (c_4 -\frac {11}{36}\right ) x^{3}+c_3 \,x^{2}+c_2 x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 40

DSolve[x^4*D[y[x],{x,4}]-4*x^3*D[y[x],{x,3}]+12*x^2*D[y[x],{x,2}]-24*x*D[y[x],x]+24*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} x^4 \log (x)+x \left (\left (-\frac {11}{36}+c_4\right ) x^3+c_3 x^2+c_2 x+c_1\right ) \]