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  3. in exercises 1–4, verify that the given for

In exercises 1–4, verify that the given formula is a solution to the initial value problem. 2....

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Basic Math

In exercises 1–4, verify that the given formula is a solution tothe initial value problem.

2. Powers of t.

b) y ′ = t^3 , y(0) = 5: y(t) = (1/5)t^(4) + 5

3. Sines and cosines.

a) x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) =sint

Answer & Explanation Solved by verified expert
3.6 Ratings (282 Votes)
Step 1we know that if function is a solution to the initial valueproblem than it must satisfies the differential equation andinitial conditionwe have y t3 and y0 5we havewe can say that yt is a solution of the differential equationof it satisfies the differential equation y t3we can write1Lets assume that y 15t4 5 hence we can saythatPut it in equation 1 we can say thatStep 2There might be a typo    See Answer
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