Internal problem ID [1564]
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 67.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (-12 x +11\right ) \sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+4*diff(y(x),x$2)-2*diff(y(x),x)-0*y(x)=exp(x)*((28+6*x)*cos(2*x)+(11-12*x)*sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{x} \sin \left (2 x \right ) x +\frac {3 \,{\mathrm e}^{x}}{2}-\frac {c_{3} \cos \left (x \right ) {\mathrm e}^{x}}{2}+\frac {c_{3} \sin \left (x \right ) {\mathrm e}^{x}}{2}+\frac {c_{2} {\mathrm e}^{x} \cos \left (x \right )}{2}+\frac {c_{2} \sin \left (x \right ) {\mathrm e}^{x}}{2}+c_{1} {\mathrm e}^{x}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.278 (sec). Leaf size: 88
DSolve[y''''[x]-3*y'''[x]+4*y''[x]-2*y'[x]-0*y[x]==Exp(x)*((28+6*x)*Cos[2*x]+(11-12*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{500} \text {Exp} \left (300 x^2+715 x+676\right ) \cos (2 x)+\frac {1}{500} \cos (x) \left (\text {Exp} \left (300 x^2-160 x-819\right ) \sin (x)-250 (c_1-c_2) e^x\right )+c_3 e^x+\frac {1}{2} c_1 e^x \sin (x)+\frac {1}{2} c_2 e^x \sin (x)+c_4 \]