explain the method employed in solving non homogeneous differential equation
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Explanation:
The nonhomogeneous differential equation of this type has the form. y′′+py′+qy=f(x), where p,q are constant numbers (that can be both as real as complex numbers). For each equation we can write the related homogeneous or complementary equation: y′′+py′+qy=0.
General Solution to a Nonhomogeneous Equation
a 2 ( x ) y ″ + a 1 ( x ) y ′ + a 0 ( x ) y = r ( x ) . a 2 ( x ) y ″ + a 1 ( x ) y ′ + a 0 ( x ) y = r ( x ) . y ( x ) = c 1 y 1 ( x ) + c 2 y 2 ( x ) + y p ( x ). y ( x ) = c 1 y 1 ( x ) + c 2 y 2 ( x ) + y p ( x )
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