What is the solution for (dy)/(dt)=2y+2t^2-10/3 t ?

The solution for (dy)/(dt)=2y+2t^2-10/3 t is y=-t^2+(2t)/3+1/3+c_{1}e^{2t}

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(dy)/(dt)=2y+2t^2-10/3 t

\frac{d y}{d t} = 2 y + 2 t^{2} - \frac{10}{3} t

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

Solution steps

\frac{d y}{d t} = 2 y + 2 t^{2} - \frac{10}{3} t

Solve linear ODE:

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

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

\int 2 z d z

x^{5} sin (x)

\frac{d}{d x} (\frac{sin ( x )}{cos ^{2} ( x )})

\frac{d}{d x} (4 - x^{\frac{2}{3}})

\frac{d}{d x} (x^{\frac{4}{3}} - 5)

What is the solution for (dy)/(dt)=2y+2t^2-10/3 t ?
The solution for (dy)/(dt)=2y+2t^2-10/3 t is y=-t^2+(2t)/3+1/3+c_{1}e^{2t}