What is the solution for (dy)/(dt)= t/(t^2y+y),y(0)=7 ?

The solution for (dy)/(dt)= t/(t^2y+y),y(0)=7 is y=sqrt(ln(t^2+1)+49)

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(dy)/(dt)= t/(t^2y+y),y(0)=7

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}, y (0) = 7

y = ln (t^{2} + 1) + 49

Solution steps

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}

Solve separable ODE:

y = ln (t^{2} + 1) + 49

y = ln (t^{2} + 1) + 49

What is the solution for (dy)/(dt)= t/(t^2y+y),y(0)=7 ?
The solution for (dy)/(dt)= t/(t^2y+y),y(0)=7 is y=sqrt(ln(t^2+1)+49)