12.20.13 problem section 9.4, problem 33

Internal problem ID [2234]
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 33
Date solved : Monday, January 27, 2025 at 05:43:54 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y&=40 x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=-1\\ y^{\prime }\left (-1\right )&=-7\\ y^{\prime \prime }\left (-1\right )&=-1\\ y^{\prime \prime \prime }\left (-1\right )&=-31 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 29

dsolve([x^4*diff(y(x),x$4)+5*x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)-6*x*diff(y(x),x)+6*y(x)=40*x^3,y(-1) = -1, D(y)(-1) = -7, (D@@2)(y)(-1) = -1, (D@@3)(y)(-1) = -31],y(x), singsol=all)
 

\[ y = \frac {x^{5} \ln \left (x \right )-1+\left (-i \pi -2\right ) x^{5}+x^{3}+x}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 32

DSolve[{x^4*D[y[x],{x,4}]+5*x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+6*y[x]==40*x^3,{y[-1]==-1,Derivative[1][y][-1]==-7,Derivative[2][y][-1]==-1,Derivative[3][y][-1]==-31}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(-2-i \pi ) x^5+x^5 \log (x)+x^3+x-1}{x^2} \]