Internal problem ID [1578]
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 22.
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 }-2 x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y-4 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 4, y^{\prime }\relax (1) = 4, y^{\prime \prime }\relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 23
dsolve([x^3*diff(y(x),x$3)-2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-3*y(x)=4*x,y(1) = 4, D(y)(1) = 4, (D@@2)(y)(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = x \left (x^{2}-\ln \relax (x )^{2}-2 \ln \relax (x )+3\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 20
DSolve[{x^3*y'''[x]-2*x^2*y''[x]+3*x*y'[x]-3*y[x]==4*x,{y[1]==4,y'[1]==4,y''[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (x^2-\log (x) (\log (x)+2)+3\right ) \\ \end{align*}