Internal problem ID [1506]
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 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y-{\mathrm e}^{2 x} \left (17+30 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 55
dsolve(2*diff(y(x),x$3)-7*diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=exp(2*x)*(17+30*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (1+2 x \right ) \left (30 \,{\mathrm e}^{2 x} x +17 \,{\mathrm e}^{2 x}\right )}{34+60 x}+c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} {\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 46
DSolve[2*y'''[x]-7*y''[x]+4*y'[x]+4*y[x]==Exp[2*x]*(17+30*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (x^3+\frac {x^2}{2}+\left (-\frac {2}{5}+c_3\right ) x+\frac {4}{25}+c_2\right )+c_1 e^{-x/2} \\ \end{align*}