Internal problem ID [1528]
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 31.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 217
dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+2*diff(y(x),x)-2*y(x)=exp(2*x)*((27+5*x-x^2)*cos(1*x)+(2+13*x+9*x^2)*sin(1*x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {5 \,{\mathrm e}^{2 x} \cos \left (x \right ) x^{2}}{3}+5 \,{\mathrm e}^{2 x} \cos \left (x \right )+\frac {10 \,{\mathrm e}^{2 x} \sin \left (x \right ) x}{3}+\frac {4 \,{\mathrm e}^{2 x} \sin \left (x \right ) x^{2}}{3}+\frac {7 \,{\mathrm e}^{2 x} \sin \left (x \right )}{3}+\frac {5 \,{\mathrm e}^{2 x} \cos \left (x \right ) x}{3}+\left (\int \frac {\sqrt {2}\, \left (\cos \left (x \right ) x^{2}-9 \sin \left (x \right ) x^{2}-5 \cos \left (x \right ) x -13 \sin \left (x \right ) x -27 \cos \left (x \right )-2 \sin \left (x \right )\right ) \left (\sqrt {2}\, \cos \left (\sqrt {2}\, x \right )-\sin \left (\sqrt {2}\, x \right )\right ) {\mathrm e}^{2 x}}{6}d x \right ) \cos \left (\sqrt {2}\, x \right )+\left (\int \frac {\sqrt {2}\, \left (\cos \left (x \right ) x^{2}-9 \sin \left (x \right ) x^{2}-5 \cos \left (x \right ) x -13 \sin \left (x \right ) x -27 \cos \left (x \right )-2 \sin \left (x \right )\right ) \left (\sqrt {2}\, \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right )\right ) {\mathrm e}^{2 x}}{6}d x \right ) \sin \left (\sqrt {2}\, x \right )+c_{1} {\mathrm e}^{x}+c_{2} \cos \left (\sqrt {2}\, x \right )+c_{3} \sin \left (\sqrt {2}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 60
DSolve[1*y'''[x]-1*y''[x]+2*y'[x]-2*y[x]==Exp[2*x]*((27+5*x-x^2)*Cos[1*x]+(2+13*x+9*x^2)*Sin[1*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (\left (-x^2+x+1\right ) \cos (x)+(2 x+1) \sin (x)\right )+c_3 e^x+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \]