Internal problem ID [13430]
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 (n).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y=3 x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=3*x^4,y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{5 x}+x \,{\mathrm e}^{5 x} c_{1} +\frac {3 x^{4}}{25}+\frac {24 x^{3}}{125}+\frac {108 x^{2}}{625}+\frac {288 x}{3125}+\frac {72}{3125} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 47
DSolve[y''[x]-10*y'[x]+25*y[x]==3*x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 \left (125 x^4+200 x^3+180 x^2+96 x+24\right )}{3125}+c_1 e^{5 x}+c_2 e^{5 x} x \]