Internal problem ID [14045]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}+\frac {3}{2} x^{2}+\frac {9}{2} x +\frac {15}{4}\right ) {\mathrm e}^{2 x}-2 c_{2} {\mathrm e}^{3 x}-2 c_{1} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 39
DSolve[y''[x]+y'[x]-2*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (-4 x^3-6 x^2-18 x-15\right )+c_1 e^{-2 x}+c_2 e^x \]