# Integrating factor differential equation pdf

We will say that a given ﬁrst-order differential equation is directly integrable if (and only if) it can be (re)written as dy dx = f(x) (2.1) where f(x) is some known function of just x (no y’s). More ## 5. Exact Equations, Integrating Factors, and Homogeneous

The integrating factor method. Proof: Multiply the diﬀerential equation y0(t)+ ay(t) = b by a non-zero function µ, that is, µ(t) y0 + ay = µ(t) b. Key idea: The non-zero function µ is called an
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## First-Order Linear Equations (Integrating Factors)

ordinary differential equations hence equation (i) is exact and its general solution is given by the formula [ terms in n (x , y) without x] dy = c m(x,y)dx+ (3x2y2+2xy)dx+ ody=c or x3y2+x2y=c or 