Internal problem ID [1582]
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 30.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y-9 x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -7, y^{\prime }\relax (1) = -11, y^{\prime \prime }\relax (1) = -5, y^{\prime \prime \prime }\relax (1) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 14
dsolve([x^4*diff(y(x),x$4)+3*x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=9*x^2,y(1) = -7, D(y)(1) = -11, (D@@2)(y)(1) = -5, (D@@3)(y)(1) = 6],y(x), singsol=all)
\[ y \relax (x ) = x^{2} \left (-7+3 \ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 15
DSolve[{x^4*y''''[x]+3*x^3*y'''[x]-x^2*y''[x]+2*x*y'[x]-2*y[x]==9*x^2,{y[1]==-7,y'[1]==-11,y''[1]==-5,y'''[1]==6}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (3 \log (x)-7) \\ \end{align*}