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Verify that y=e^-x+Ax+B is a solution of the diffrential equation e^x (d^2y) =1
                                                                                          (dx^2)

Asked by aadeshpdabre 23rd May 2016, 2:51 PM
Answered by Expert
Answer:
C o n s i d e r space t h e space g i v e n space f u n c t i o n comma space y equals e to the power of negative x end exponent plus A x plus B
D i f f e r e n t i a t i n g space t h e space a b o v e space e q u a t i o n space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma
fraction numerator d y over denominator d x end fraction equals negative e to the power of negative x end exponent plus A
D i f f e r e n t i a t i n g space o n c e space a g a i n comma space w e space h a v e comma
fraction numerator d squared y over denominator d x squared end fraction equals e to the power of negative x end exponent
rightwards double arrow e to the power of x cross times fraction numerator d squared y over denominator d x squared end fraction equals e to the power of x cross times e to the power of negative x end exponent
rightwards double arrow e to the power of x cross times fraction numerator d squared y over denominator d x squared end fraction equals 1
T h u s comma space y equals space y equals e to the power of negative x end exponent plus A x plus B space i s space t h e space s o l u t i o n space o f space e to the power of x cross times fraction numerator d squared y over denominator d x squared end fraction equals 1
Answered by Expert 24th May 2016, 5:22 PM
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