Internal problem ID [13429]
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 (m).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=3 x^{2} {\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=3*x^2*exp(5*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{5 x}+x \,{\mathrm e}^{5 x} c_{1} +\frac {x^{4} {\mathrm e}^{5 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 27
DSolve[y''[x]-10*y'[x]+25*y[x]==3*x^2*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{5 x} \left (x^4+4 c_2 x+4 c_1\right ) \]