I think my book is giving me the wrong answer....The problem is to find solution of following:(adsbygoogle = window.adsbygoogle || []).push({});

r'(t) = t^{2}[itex]\hat{i}[/itex] + 5t[itex]\hat{j}[/itex] + [itex]\hat{k}[/itex]

The initial condition is:

r(1) = [itex]\hat{j}[/itex] + 2[itex]\hat{k}[/itex]

My solution:

r(t) = < (1/3)t^{3}+ c_{1}, (5/2)t^{2}+ c_{2}, t+c_{3}>

r(1) = < 0 , 1 , 2 >

r(1) = < (1/3)+c_{1}, (5/2)+c_{2}, 1+c_{3}>

Therefore:

< 0 , 1 , 2 > = < (1/3)+c_{1}, (5/2)+c_{2}, 1+c_{3}>

Solving for the three c's yields:

c_{1}= -(1/3)

c_{2}= -1.5

c_{3}= 1

And so the solution with the initial conditions is:

< (1/3)t^{3}- (1/3) , (5/2)t^{2}-1.5 , t+1 >

My book gives the solution as:

< (1/3)t^{3}, (5/2)t^{2}+ 1 , t+2 >

Who is right?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Solution of differential with initial conditions

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