Determine the form of a particular solution to L(y)=phi (x) for phi(x) as given if the solution to the associated homogeneous equation L(y)=0 is y_h=c_1 e^(2x)+c_2 e^(3x) 1) phi(x)=2x-7 2) phi(x)=-3x^2 3) phi(x)=4e^(2x) 4) phi(x)=2 cos (3x)

stratsticks57jl 2022-07-20 Answered
Determine the form of a particular solution to L ( y ) = ϕ ( x ) for ϕ ( x ) as given if the solution to the associated homogeneous equation L(y)=0 is y h = c 1 e 2 x + c 2 e 3 x
1 ) ϕ ( x ) = 2 x 7 2 ) ϕ ( x ) = 3 x 2 3 ) ϕ ( x ) = 4 e 2 x 4 ) ϕ ( x ) = 2 cos ( 3 x )
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fairymischiefv9
Answered 2022-07-21 Author has 11 answers
Consider the differential equation
L [ y ] = ϕ ( x )
The complementary solution associated with L[y] is y h = c 1 e 2 x + c 2 e 3 x
1)Find the form of particularsolution if This function is polynomial and no repetition of terms with y h , the form of particular solution is y p ( x ) = A x + B
2)Find the form of particularsolutionif ϕ ( x ) = 3 x 2 This function is polynomial and no repetition of terms with y h , the form of particular solution is y p ( x ) = A x 2 + B x + C
3)Find the form of particularsolution if ϕ ( x ) = 4 e 2 x This function is exponential and thereis repetition of terms with y h ( c 1 e 2 x ), the form of particular solution is y p ( x ) = x A e 2 x ,(if there is no repetition then the particular solution form is y p ( x ) = A e 2 x
4)Find the form of particular solution if ϕ ( x ) = 2 cos 3 xThis function is trigonometric and there is no repetition of terms with y h , the form of particular solution is y p ( x ) = A cos 3 x + B sin 3 x

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