What is the solution for 3y^'-8y=e^{-pit^2},y(0)=a ?

The solution for 3y^'-8y=e^{-pit^2},y(0)=a is y=e^{(8t)/3}*integral of (e^{(-3pit^2-8t)/3})/(3)

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3y^'-8y=e^{-pit^2},y(0)=a

3 y^{^{'}} - 8 y = e^{- π t^{2}}, y (0) = a

y = e^{\frac{8 t}{3}} \cdot \int \frac{e ^{\frac{- 3 π t ^{2} - 8 t}{3}}}{3} d t

Solution steps

3 y^{'} (t) - 8 y = e^{- π t^{2}}

Solve linear ODE:

y = e^{\frac{8 t}{3}} \cdot \int \frac{e ^{\frac{- 3 π t ^{2} - 8 t}{3}}}{3} d t

y = e^{\frac{8 t}{3}} \cdot \int \frac{e ^{\frac{- 3 π t ^{2} - 8 t}{3}}}{3} d t

What is the solution for 3y^'-8y=e^{-pit^2},y(0)=a ?
The solution for 3y^'-8y=e^{-pit^2},y(0)=a is y=e^{(8t)/3}*integral of (e^{(-3pit^2-8t)/3})/(3)