Internal problem ID [13739]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.11 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*exp(-7*x)+2*exp(-7*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-7 x} \left (x^{2}+90 \,{\mathrm e}^{9 x} c_{1} +90 c_{2} {\mathrm e}^{10 x}+\frac {19 x}{45}+\frac {8371}{4050}\right )}{90} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 41
DSolve[y''[x]-5*y'[x]+6*y[x]==x^2*Exp[-7*x]+2*Exp[-7*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-7 x} \left (4050 x^2+1710 x+8371\right )}{364500}+c_1 e^{2 x}+c_2 e^{3 x} \]