12.20.9 problem section 9.4, problem 25

Internal problem ID [2230]
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 25
Date solved : Monday, January 27, 2025 at 05:43:51 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y&=9 x^{4} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=1\\ y^{\prime \prime }\left (1\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 29

dsolve([x^3*diff(y(x),x$3)-6*x^2*diff(y(x),x$2)+16*x*diff(y(x),x)-16*y(x)=9*x^4,y(1) = 2, D(y)(1) = 1, (D@@2)(y)(1) = 5],y(x), singsol=all)
 

\[ y = -x^{4}+\frac {3 \ln \left (x \right )^{2} x^{4}}{2}+2 \ln \left (x \right ) x^{4}+3 x \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 32

DSolve[{x^3*D[y[x],{x,3}]-6*x^2*D[y[x],{x,2}]+16*x*D[y[x],x]-16*y[x]==9*x^4,{y[1]==2,Derivative[1][y][1]==1,Derivative[2][y][1]==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x^4+\frac {3}{2} x^4 \log ^2(x)+2 x^4 \log (x)+3 x \]