12.20.11 problem section 9.4, problem 30

Internal problem ID [2232]
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 30
Date solved : Monday, January 27, 2025 at 05:43:52 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=9 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-7\\ y^{\prime }\left (1\right )&=-11\\ y^{\prime \prime }\left (1\right )&=-5\\ y^{\prime \prime \prime }\left (1\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 14

dsolve([x^4*diff(y(x),x$4)+3*x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=9*x^2,y(1) = -7, D(y)(1) = -11, (D@@2)(y)(1) = -5, (D@@3)(y)(1) = 6],y(x), singsol=all)
 

\[ y = x^{2} \left (-7+3 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 15

DSolve[{x^4*D[y[x],{x,4}]+3*x^3*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-2*y[x]==9*x^2,{y[1]==-7,Derivative[1][y][1]==-11,Derivative[2][y][1]==-5,Derivative[3][y][1]==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (3 \log (x)-7) \]