What is the solution for 2t((dy)/(dt))+y=4t^2+3t ?

The solution for 2t((dy)/(dt))+y=4t^2+3t is y=(4t^2)/5+t+(c_{1})/(sqrt(t))

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2t((dy)/(dt))+y=4t^2+3t

2 t (\frac{d y}{d t}) + y = 4 t^{2} + 3 t

y = \frac{4 t ^{2}}{5} + t + \frac{c _{1}}{t}

Solution steps

2 t (\frac{d y}{d t}) + y = 4 t^{2} + 3 t

Solve linear ODE:

y = \frac{4 t ^{2}}{5} + t + \frac{c _{1}}{t}

y = \frac{4 t ^{2}}{5} + t + \frac{c _{1}}{t}

\int_{2}^{3} \frac{5}{x ^{2} - 1} d x

\int \frac{1}{e ^{x}} d x

\frac{d x}{d t} = 2 x

x \to \infty lim 1 + \frac{1}{x} - 1 x

y^{^{'}} = e^{x - y}

What is the solution for 2t((dy)/(dt))+y=4t^2+3t ?
The solution for 2t((dy)/(dt))+y=4t^2+3t is y=(4t^2)/5+t+(c_{1})/(sqrt(t))