1. Consider the initial value problem +5y = cost, y(0) = 1. Solve the IVP...

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1. Consider the initial value problem 분 +5y = cost, y(0) = 1. Solve the IVP using THREE DIFFERENT METHODS. 2. Solve the following differential equations. If there are initial values, solve the IVP. If there are not, find the general solution. (a) (2x + y)dr + (2y+z)dy = 0, y(2) = -3; (b) (lnx+3y²) + (w/1) = 0: (c) (1 + y²) 2ry + 4y 3. Solve the following initial value problems: y" + 5y +6y=sin(t), y(0) = 1, g(0) = 0. (b) y" +2y + 5y-0. y(0)=-1. y(0) = 4. (c) y" +9y+6y=e3, y(0) = 3, y'(0) = 2. y"+9y+6y=t², y(0) = 0, y'(0) = 0. (d) 1. Consider the initial value problem 분 +5y = cost, y(0) = 1. Solve the IVP using THREE DIFFERENT METHODS. 2. Solve the following differential equations. If there are initial values, solve the IVP. If there are not, find the general solution. (a) (2x + y)dr + (2y+z)dy = 0, y(2) = -3; (b) (lnx+3y²) + (w/1) = 0: (c) (1 + y²) 2ry + 4y 3. Solve the following initial value problems: y" + 5y +6y=sin(t), y(0) = 1, g(0) = 0. (b) y" +2y + 5y-0. y(0)=-1. y(0) = 4. (c) y" +9y+6y=e3, y(0) = 3, y'(0) = 2. y"+9y+6y=t², y(0) = 0, y'(0) = 0. (d)

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