Internal problem ID [1521]
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 24.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime }-{\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 76
dsolve(1*diff(y(x),x$4)-3*diff(y(x),x$3)-0*diff(y(x),x$2)+4*diff(y(x),x)+0*y(x)=exp(2*x)*(15+26*x+12*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{2} {\mathrm e}^{2 x}}{2}-{\mathrm e}^{-x} c_{1}+\frac {{\mathrm e}^{2 x} x^{3}}{6}+c_{3} \left (\frac {{\mathrm e}^{2 x} x}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )+\frac {{\mathrm e}^{2 x} x^{4}}{6}+\frac {{\mathrm e}^{2 x} x^{2}}{2}-\frac {{\mathrm e}^{2 x} x}{2}+\frac {{\mathrm e}^{2 x}}{4}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 54
DSolve[1*y''''[x]-3*y'''[x]-0*y''[x]+4*y'[x]+0*y[x]==Exp[2*x]*(15+26*x+12*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} e^{2 x} \left (2 x \left (x \left (x^2+x+3\right )-6\right )+3 c_3 (2 x-1)+8+6 c_2\right )+c_1 \left (-e^{-x}\right )+c_4 \\ \end{align*}