3.8 problem 8

Internal problem ID [5187]

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]]

Solve \begin {gather*} \boxed {y^{\prime }+2 y-b \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

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

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

Solution by Mathematica

Time used: 0.046 (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*}