Internal problem ID [12454]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number: 1.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y=2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 78
dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)+13*diff(y(x),x$2)-12*diff(y(x),x)+4*y(x)=2*exp(x)-4*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\left (-x^{2} {\mathrm e}^{2 x}+2 x^{2} {\mathrm e}^{3 x}+12 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{2 x} x -8 x \,{\mathrm e}^{3 x}-6 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+x \,{\mathrm e}^{x} c_{3} +x \,{\mathrm e}^{2 x} c_{4} \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 41
DSolve[y''''[x]-6*y'''[x]+13*y''[x]-12*y'[x]+4*y[x]==2*Exp[x]-4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (x^2+e^x \left (-2 x^2+(8+c_4) x-12+c_3\right )+(4+c_2) x+6+c_1\right ) \]