1. Solve the following second-order ODE and then use the boundary and initial conditions to complete...

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1. Solve the following second-order ODE and then use the boundary and initial conditions to complete the solution. 1 e³-e -x (b) y" — y = e* cos2x, y(0) = 1,y'(0) = 0. . . ans. y = C₁e* + С₂e¯* + 1⁄e* (sin2x – cos2x), C₁ = 1, C₂ = (a)y" - 4y' + 3y = 0,y(0) = 0,y(1) = 1... ans. y = C₁e³x + С₂еx,C₁ 3x -C₂ == = 1. Solve the following second-order ODE and then use the boundary and initial conditions to complete the solution. 1 e³-e -x (b) y" — y = e* cos2x, y(0) = 1,y'(0) = 0. . . ans. y = C₁e* + С₂e¯* + 1⁄e* (sin2x – cos2x), C₁ = 1, C₂ = (a)y" - 4y' + 3y = 0,y(0) = 0,y(1) = 1... ans. y = C₁e³x + С₂еx,C₁ 3x -C₂ == =