Internal problem ID [1514]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 17.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y-{\mathrm e}^{x} \left (x^{2}+4 x +3\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 118
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+0*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x)*(3+4*x+x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x +1\right ) \left (x^{2} {\mathrm e}^{x}+4 x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{x}\right )}{x +3}+c_{1} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \mathit {index} =1\right ) x}+c_{2} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \mathit {index} =2\right ) x}+c_{3} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \mathit {index} =3\right ) x}+c_{4} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \mathit {index} =4\right ) x} \]
✓ Solution by Mathematica
Time used: 1.905 (sec). Leaf size: 1533
DSolve[y''''[x]-2*y'''[x]+0*y''[x]+3*y'[x]-y[x]==Exp[x]*(3+4*x+x^2),y[x],x,IncludeSingularSolutions -> True]
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