Internal problem ID [5932]
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: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y a=b \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x)+a*y(x)=b(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\int b \left (x \right ) {\mathrm e}^{a x}d x +c_{1} \right ) {\mathrm e}^{-a x} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 32
DSolve[y'[x]+a*y[x]==b[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-a x} \left (\int _1^xe^{a K[1]} b(K[1])dK[1]+c_1\right ) \]