Internal problem ID [13707]
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: 22.5 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }-5 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+4*diff(y(x),x)-5*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-5 x} \left (\left (x^{3}+\frac {12}{5} x^{2}+\frac {126}{25} x +\frac {624}{125}\right ) {\mathrm e}^{5 x}-5 \,{\mathrm e}^{6 x} c_{2} -5 c_{1} \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 39
DSolve[y''[x]+4*y'[x]-5*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{625} \left (-125 x^3-300 x^2-630 x-624\right )+c_1 e^{-5 x}+c_2 e^x \]