What is the solution for y^'+e^yt=e^ysin(t) ?

The solution for y^'+e^yt=e^ysin(t) is y=-ln(cos(t)+(t^2)/2-c_{1})

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y^'+e^yt=e^ysin(t)

y^{^{'}} + e^{y} t = e^{y} sin (t)

y = - ln (cos (t) + \frac{t ^{2}}{2} - c_{1})

Solution steps

y^{'} (t) + e^{y} t = e^{y} sin (t)

Solve separable ODE:

y = - ln (cos (t) + \frac{t ^{2}}{2} - c_{1})

y = - ln (cos (t) + \frac{t ^{2}}{2} - c_{1})

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\int_{0}^{π} cos^{4} (x) d x

What is the solution for y^'+e^yt=e^ysin(t) ?
The solution for y^'+e^yt=e^ysin(t) is y=-ln(cos(t)+(t^2)/2-c_{1})