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  • Find the differential equation corresponding to y=ae^2x+be^-3x+ce^x where a,b , are arbitrary constants

Find the differential equation corresponding to y=ae^2x+be^-3x+ce^x where a,b , are arbitrary constants

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Solution: We have ,

y=ae^2x+be^-3x+ce^x ............(1)\ \Rightarrow y_1 =2ae^2x-3be^-3x+ce^x ..........(2)\ \Rightarrow y_2=4ae^2x+9be^-3x+ce^x .........(3)\ \Rightarrow y_3=8ae^2x-27be^-3x+ce^x .............(4)

Form Equation (1), (2),(3);and(4)

Requried differential equation is , 

y_3-7y_1+6y=0

Posted by

Deependra Verma

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