monty981
monty981
12-05-2017
Mathematics
contestada
Solve Differential Equation
y' = 4 x + 7 y
Respuesta :
LammettHash
LammettHash
12-05-2017
[tex]y'=4x+7y[/tex]
[tex]y'-7y=4x[/tex]
[tex]e^{-7x}y'-7e^{-7x}y=4xe^{-7x}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[e^{-7x}y\right]=4xe^{-7x}[/tex]
[tex]e^{-7x}y=\displaystyle\int4xe^{-7x}\,\mathrm dx[/tex]
[tex]e^{-7x}y=-\dfrac47xe^{-7x}-\dfrac4{49}e^{-7x}+C[/tex]
[tex]y=-\dfrac47x-\dfrac4{49}+Ce^{7x}[/tex]
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