Internal problem ID [10267]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 12.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y-{\mathrm e}^{3 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)-diff(y(x),x$3)-3*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{3 x}}{40}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} x \,{\mathrm e}^{x}+c_{4} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 39
DSolve[y''''[x]-y'''[x]-3*y''[x]+5*y'[x]-2*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{3 x}}{40}+c_1 e^{-2 x}+e^x (x (c_4 x+c_3)+c_2) \\ \end{align*}