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  • Find the diffrential equation whose solution represents the family : y=acos(theta)x+bsin(theta)x, where theta =fixed constant

Find the diffrential equation whose solution represents the family : y=acos(theta)x+bsin(theta)x, where theta =fixed constant

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Solution:     y=acos heta x+bsin heta x  ,       \ heta = fixed constant

                   Diffrentiating  ,we get        fracmathrmd ymathrmd x=-a heta sin heta x+b heta cos heta x

                 Again diffrentiating  , we get      fracmathrmd ^2ymathrmd x^2=- heta ^2acos heta x- heta ^2bsin heta x

                  Hence ,            fracmathrmd ^2ymathrmd x^2=- heta ^2y

Posted by

Deependra Verma

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