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GIVEN problem; dy/dx-2Y=Ce^1/3xX Obtained solution: Y= - 3/5 Ce^1/3xX+ B e^2X Request the steps adapted in arriving at the solution in detail . Thanks

GIVEN problem;   dy/dx-2Y=Ce^1/3xX                                                                                                                                     Obtained solution:   Y= - 3/5 Ce^1/3xX+ B e^2X                         Request the steps adapted in arriving at the solution in detail . Thanks                                                                                  

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1 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

let dy/dx+ p(x)y=r(x), integrating factor of this linear differential equation is e^((indefinite)integralp(x)dx) denoted as e^h ,

e^h(y'+py)=d(hy)/dx=(e^h)r(x)

(e^h)y=indef.intgrl((e^h)rdx +c)

y(x)=(e^-h)(indef.intgrl((e^h)rdx +c))

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