Write the value of y(1) if y is the solution of e^t dy/dt+e^ty=t, y(0)=1, round your answer to four digits after the decimal sign

Step-by-step explanation:

Given the differential equation

From the equation;

The resulting equation is a first order differential equation in the form

dy/dt + p(t)y = q(t)

The solution to the DE will be in the form yI = where I is the integrating factor expressed as

From the DE above p(t ) = 1 and q(t) =

The solution to the DE will become

If y(0) = 1 then;

The value of y(1) will be expressed as;