Internal problem ID [1586]
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 36.
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-F \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 37
dsolve(x^3*diff(y(x),x$3)+x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=F(x),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{3}+\int \frac {c_{2}-\left (\int -\frac {c_{1}-\left (\int -F \relax (x )d x \right )}{x^{3}}d x \right )}{x^{2}}d x \right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 80
DSolve[x^3*y'''[x]+x^2*y''[x]-2*x*y'[x]+2*y[x]==f[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 \left (\int _1^x-\frac {f(K[2])}{2 K[2]^2}dK[2]+x \int _1^x\frac {f(K[3])}{3 K[3]^3}dK[3]\right )+\int _1^x\frac {1}{6} f(K[1])dK[1]+x^2 (c_3 x+c_2)+c_1}{x} \\ \end{align*}