Internal problem ID [1580]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 y^{\prime } x -16 y-9 x^{4}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 1, y^{\prime \prime }\relax (1) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.027 (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)
\[ y \relax (x ) = -x^{4}+\frac {3 \ln \relax (x )^{2} x^{4}}{2}+2 \ln \relax (x ) x^{4}+3 x \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 29
DSolve[{x^3*y'''[x]-6*x^2*y''[x]+16*x*y'[x]-16*y[x]==9*x^4,{y[1]==2,y'[1]==1,y''[1]==5}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x^4 \log (x) (3 \log (x)+4)-x \left (x^3-3\right ) \\ \end{align*}