Internal problem ID [5186]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y-b \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x)+2*y(x)=b(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\int b \left (x \right ) {\mathrm e}^{2 x}d x +c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 31
DSolve[y'[x]+2*y[x]==b[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (\int _1^xe^{2 K[1]} b(K[1])dK[1]+c_1\right ) \\ \end{align*}