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Grade 12Differential Calculus

Please solve the following problem,

Verify that y = C*e 4x + e 3x, where c is a constant, is a solution to the differential equation y ' - 4y = -e 3x .

Profile image of swati shrivastav
17 Years agoGrade 12
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1 Answer

Profile image of anjali SHARMA
17 Years ago

Hi Swati please follow the following:

y ' is given by

y ' = 4C*e 4x + 3e 3x

We now substitute y ' and y into the left side of the equation and simplify

y ' - 4y = 4C*e 4x + 3e 3x - 4 (C*e 4x + e 3x)

= 4C*e 4x + 3e 3x - 4C*e 4x - 4e 3x

= 4C*e 4x - 4C*e 4x + e 3x (3 - 4)

= - e 3x

 

enjoy...

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