Question

The answer above is NOT correct 1 point) Solve the following initial value problem dy dt with y(0) = 4. Preview My AnswersSubmit Answers Your score was recorded You have attempted this problem 8 times You received a score of 0% for this attempt >Your overall recorded score is 0% You have unlimited attempts remaining Email instructor rch 16回 17

Answer 1

Solve the following initial value problem dy/dt = 0.5ty = 3t with y(0) = 4 this is a linear differential equation so, we calculate integrating factors here integrating factor (I.F) = e^integrating0.5dt = e^0.5t^2 = e^0.25t^2 now, general solution is given as y(e^0.25t^2) = integrale^0.25t^2 3t dt put 0.25 t^2 = u 0.50 t at = du ye^0.25t^2 = 3/0.5 integral e^u du = 30/5 e^u + c ye^0.25t^2 = 6e^0.25t^2 + c y(t0 = 6 + ce^-0.25t^2 put t = 0 & y = -4 in 1 we get y = 6 + c c = -2 \r\n Hence, the solution is y(t = 6 - 2e^-0.25t^2