49.2.3 problem 1(c)

Internal problem ID [7593]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:06:57 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=x^{2}+x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x)-2*y(x)=x^2+x,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} c_{1} -\frac {\left (x +1\right )^{2}}{2} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 23

DSolve[D[y[x],x]-2*y[x]==x^2+x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} (x+1)^2+c_1 e^{2 x} \]