Question: 2. Solve the following differential equation with the given initial value. dy = x6, y(1) = 0 dx O y = O y = O

2. Solve the following differential equation with the given initial value. dy = x6, y(1) = 0 dx O y = O y = O y = + O y E + CD ) 3.A 21-year-old student is offered an opportunity to invest some money in a retirement account that pays 9% annual interest compounded continuously. How much does the student need to invest today to have $1 million when she retires at age 65? What if she could earn 10% annual interest compounded continuously instead? () $17422.37,$11109.00 () $40212972.15, $39812846.39 () $19063.11,$12277.34 (O $20771.16, $20564.49 4. Solve the following differential equation by separation of variables. dy = 5x tan(y) dx O y = sin 1 (e527/7) + C O y = sin (eC+527/7) O y= eC+ 5a7 /7 O y = eba'/7 + C\f1. Show that y = 3est + 2 sin x is a solution of the initial value problem y - 3y = 2 cos x - 6 sin x, with y(0) = 3

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