Internal problem ID [1577]
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 18.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y-12 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 39
dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+4*y(x)=12*x^2,y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+c_{3} x +\frac {c_{4}}{x^{2}}+\frac {12 x^{3} \ln \relax (x )-15 x^{3}+2 c_{1}}{12 x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 38
DSolve[x^4*y''''[x]+6*x^3*y'''[x]+2*x^2*y''[x]-4*x*y'[x]+4*y[x]==12*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^4 \log (x)+\left (-\frac {19}{12}+c_4\right ) x^4+c_3 x^3+c_2 x+c_1}{x^2} \\ \end{align*}