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    Say we have a second order ODE

    ay'' + by' + cy = f(x) + g(x)

    where f(x) and g(x) are functions of x.

    And say we want to find a particular integral for this.

    What if we find a particular integral to
    ay'' + by' + cy = f(x)
    and one to
    ay'' + by' + cy = g(x)
    ?

    If we add together these particular integrals will we get a particular integral for
    ay'' + by' + cy = f(x) + g(x)
    ?
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    (Original post by gangsta316)
    Say we have a second order ODE

    ay'' + by' + cy = f(x) + g(x)

    where f(x) and g(x) are functions of x.

    And say we want to find a particular integral for this.

    What if we find a particular integral to
    ay'' + by' + cy = f(x)
    and one to
    ay'' + by' + cy = g(x)
    ?

    If we add together these particular integrals will we get a particular integral for
    ay'' + by' + cy = f(x) + g(x)
    ?
    Write the differential operator as L. L is linear from the chain rule.

    then if L(y)=f(x) and L(w)=g(x)

    then L(y+w) = L(y) + L(w) = f(x) + g(x)
 
 
 
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