What is the solution for (dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1) ?

The solution for (dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1) is y=(c_{1})/((t^2+1)^{3/2)}+2

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(dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1)

\frac{d y}{d t} + \frac{3 t}{t ^{2} + 1} y = \frac{6 t}{t ^{2} + 1}

y = \frac{c _{1}}{( t ^{2} + 1 ) ^{\frac{3}{2}}} + 2

Solution steps

\frac{d y}{d t} + \frac{3 t}{t ^{2} + 1} y = \frac{6 t}{t ^{2} + 1}

Solve separable ODE:

y = \frac{c _{1}}{( t ^{2} + 1 ) ^{\frac{3}{2}}} + 2

y = \frac{c _{1}}{( t ^{2} + 1 ) ^{\frac{3}{2}}} + 2

What is the solution for (dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1) ?
The solution for (dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1) is y=(c_{1})/((t^2+1)^{3/2)}+2