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Question

# Which of the following is/are a solution of the differential equation dydx=ex ?

A
y = ex
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B
y = ex
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C
y = ex+1
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D
y = ex-1
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Solution

## The correct option is C y = ex+1y=f(x) is a solution of the differentialequation if it satisfies the equation.Substitute each of the given y(x) inthe DE to find out which is/are the solution(s). For y=ex, dydx=d(ex)dx= ex which is equal to the RHS of the DE.Hence y=ex is a solution ofthe given DE.For y=e−x,dydx=d(e−x)dx= −e−x which isnot equal to the RHS of the DE.Hence y=e−x is not a solution ofthe given DE.Similarly we can check for theother 2 options.

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