Internal problem ID [1579]
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 23.
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 }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y-x^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0, y^{\prime }\relax (1) = 1, y^{\prime \prime }\relax (1) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 25
dsolve([x^3*diff(y(x),x$3)-5*x^2*diff(y(x),x$2)+14*x*diff(y(x),x)-18*y(x)=x^3,y(1) = 0, D(y)(1) = 1, (D@@2)(y)(1) = 7],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (\ln \relax (x )^{2} x +4 x \ln \relax (x )-2 x +2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 25
DSolve[{x^3*y'''[x]-5*x^2*y''[x]+14*x*y'[x]-18*y[x]==x^3,{y[1]==0,y'[1]==1,y''[1]==7}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x^2 (-2 x+x \log (x) (\log (x)+4)+2) \\ \end{align*}