Internal problem ID [1576]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 y^{\prime } x +24 y-x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 35
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)
\[ y \relax (x ) = -\frac {11 x^{4}}{36}+\frac {\ln \relax (x ) x^{4}}{6}+c_{4} x^{4}+c_{3} x^{3}+x^{2} c_{2}+x c_{1} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 38
DSolve[x^4*y''''[x]-4*x^3*y'''[x]+12*x^2*y''[x]-24*x*y'[x]+24*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} x^4 \log (x)+x \left (x \left (x \left (\left (-\frac {11}{36}+c_4\right ) x+c_3\right )+c_2\right )+c_1\right ) \\ \end{align*}