12.20.6 problem section 9.4, problem 18

Internal problem ID [2227]
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
Date solved : Monday, January 27, 2025 at 05:43:49 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=12 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = \frac {12 \ln \left (x \right ) x^{4}+\left (12 c_2 -15\right ) x^{4}+12 c_3 \,x^{3}+2 c_1 x +12 c_4}{12 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 38

DSolve[x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==12*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4 \log (x)+\left (-\frac {19}{12}+c_4\right ) x^4+c_3 x^3+c_2 x+c_1}{x^2} \]