solve first order linear differential equation with Integration factor method
let v(x)=∫p(x)dx
The integration factor is I=ev(x).
d[ev(x)y(x)]dx=ev(x)[dydx+p(x)y(x)]=ev(x)q(x)
The solution of the differential equation is
y(x)=e−v(x)[∫ev(x)q(x)dx+C]
[I(x)y]′=I(x)q(x)
∫xx0[I(x)y]′dx=I(x)y(x)−I(x0)y(x0)=∫xx0I(x)q(x)dx
y(x)=I(x)−1[I(x0)y(x0)+∫xx0I(x)q(x)dx]
Reference:
http://mathworld.wolfram.com/IntegratingFactor.html
https://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-LinearDiffEqns_Stu.pdf
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