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]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y=x^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1, y^{\prime \prime }\left (1\right ) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = \frac {x^{2} \left (\ln \left (x \right )^{2} x +4 x \ln \left (x \right )-2 x +2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 28
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]
\[ y(x)\to \frac {1}{2} x^2 \left (-2 x+x \log ^2(x)+4 x \log (x)+2\right ) \]