Internal problem ID [13423]
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 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} {\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*exp(3*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+\frac {x \left (x^{2}-3 x +6\right ) {\mathrm e}^{3 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 40
DSolve[y''[x]-5*y'[x]+6*y[x]==x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{2 x} \left (e^x \left (x^3-3 x^2+6 x-6+3 c_2\right )+3 c_1\right ) \]