Solve by using the Laplace Transform Method? y'+y=6e^{t^{2}},\ \ \ y(0)=3

Reginald Metcalf

Reginald Metcalf

Answered question

2022-01-21

Solve by using the Laplace Transform Method?
y+y=6et2,   y(0)=3

Answer & Explanation

Laura Worden

Laura Worden

Beginner2022-01-21Added 45 answers

Given first order differential equation
y+y=6et2, (i)
y(0)=3
claim- to check whether the differential equation can be solved using laplace transform or not
solution
applying laplace both sided
L|y|+L|y|=L|6et2|
as we know
L|y|=sy(s)y(0)
L|y|=y(s)
equation (i) becomes,
sy(s)y(0)+y(s)=6L[et2]
L[et2]=12πes24erf(π2)12iπes24
thus, we get that the first order differential equation cannot be solved using laplace transform, because the laplace transform of right hand side is not in the form of standard function.

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