Internal problem ID [1581]
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 27.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x \left (x +1\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (-1\right ) = -6, y^{\prime }\left (-1\right ) = {\frac {43}{6}}, y^{\prime \prime }\left (-1\right ) = -{\frac {5}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 30
dsolve([x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=x*(x+1),y(-1) = -6, D(y)(-1) = 43/6, (D@@2)(y)(-1) = -5/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (-2 i \pi x +2 x \ln \relax (x )+3 i \pi -3 \ln \relax (x )-12 x +24\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 34
DSolve[{x^3*y'''[x]+x^2*y''[x]-2*x*y'[x]+2*y[x]==x*(x+1),{y[-1]==-6,y'[-1]==43/6,y''[-1]==-5/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} x (i \pi (3-2 x)-12 (x-2)+(2 x-3) \log (x)) \\ \end{align*}