Internal problem ID [13400]
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: 22.9 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+4*diff(y(x),x)=x^2,y(x), singsol=all)
\[ y = -\frac {x^{2}}{16}+\frac {x^{3}}{12}-\frac {{\mathrm e}^{-4 x} c_{1}}{4}+\frac {x}{32}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 36
DSolve[y''[x]+4*y'[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{96} \left (8 x^3-6 x^2+3 x-24 c_1 e^{-4 x}+96 c_2\right ) \]