Internal problem ID [1541]
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 44.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y={\mathrm e}^{x} \left (\left (8 x +7\right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(1*diff(y(x),x$4)-5*diff(y(x),x$3)+13*diff(y(x),x$2)-19*diff(y(x),x)+10*y(x)=exp(x)*((7+8*x)*cos(2*x)+(8-4*x)*sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (x^{2}+x -4 c_{4} +\frac {23}{4}\right ) \sin \left (2 x \right )}{4}+\frac {\left (4 c_{3} +3\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{4}+c_{2} {\mathrm e}^{2 x}+\frac {{\mathrm e}^{x} \left (2 c_{1} +7\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 172
DSolve[1*y''''[x]-5*y'''[x]+13*y''[x]-19*y'[x]-10*y[x]==Exp[x]*((7+8*x)*Cos[2*x]+(8-4*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-5 \text {$\#$1}^3+13 \text {$\#$1}^2-19 \text {$\#$1}-10\&,1\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-5 \text {$\#$1}^3+13 \text {$\#$1}^2-19 \text {$\#$1}-10\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-5 \text {$\#$1}^3+13 \text {$\#$1}^2-19 \text {$\#$1}-10\&,4\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-5 \text {$\#$1}^3+13 \text {$\#$1}^2-19 \text {$\#$1}-10\&,2\right ]\right )-\frac {1}{100} e^x (-20 x \sin (2 x)+64 \sin (2 x)+40 x \cos (2 x)+67 \cos (2 x)) \]