Internal problem ID [13514]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-12 y^{\prime }+36 y=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=3*x*exp(6*x)-2*exp(6*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{6 x} c_{2} +{\mathrm e}^{6 x} x c_{1} +\frac {{\mathrm e}^{6 x} x \left (9 x^{2}-18 x +8\right )}{18} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 32
DSolve[y''[x]-12*y'[x]+36*y[x]==3*x*Exp[6*x]-2*Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{6 x} \left (x^3-2 x^2+2 c_2 x+2 c_1\right ) \]