What is the solution for 2t*(dy)/(dt)-4y=sqrt(t) ?

The solution for 2t*(dy)/(dt)-4y=sqrt(t) is y=-(t^{1/2})/3+c_{1}t^2

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2t*(dy)/(dt)-4y=sqrt(t)

2 t \cdot \frac{d y}{d t} - 4 y = t

y = - \frac{t ^{\frac{1}{2}}}{3} + c_{1} t^{2}

Solution steps

2 t \cdot \frac{d y}{d t} - 4 y = t

Solve linear ODE:

y = - \frac{t ^{\frac{1}{2}}}{3} + c_{1} t^{2}

y = - \frac{t ^{\frac{1}{2}}}{3} + c_{1} t^{2}

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(8 y^{2} - x y) d x + x^{2} d y = 0

(e^{x} sin (x))^{^{'}}

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(x^{2} - 5 x + 8) (3 x^{2} - 2)

What is the solution for 2t*(dy)/(dt)-4y=sqrt(t) ?
The solution for 2t*(dy)/(dt)-4y=sqrt(t) is y=-(t^{1/2})/3+c_{1}t^2