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Simplifying (D2 + 3d + 2) * y = e5x + 2 Reorder the terms: (2 + D2 + 3d) * y = e5x + 2 Reorder the terms for easier multiplication: y(2 + D2 + 3d) = e5x + 2 (2 * y + D2 * y + 3d * y) = e5x + 2 Reorder the terms: (3dy + 2y + yD2) = e5x + 2 (3dy + 2y + yD2) = e5x + 2 Reorder the terms: 3dy + 2y + yD2 = 2 + e5x Solving 3dy + 2y + yD2 = 2 + e5x Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2y' to each side of the equation. 3dy + 2y + -2y + yD2 = 2 + e5x + -2y Combine like terms: 2y + -2y = 0 3dy + 0 + yD2 = 2 + e5x + -2y 3dy + yD2 = 2 + e5x + -2y Add '-1yD2' to each side of the equation. 3dy + yD2 + -1yD2 = 2 + e5x + -2y + -1yD2 Combine like terms: yD2 + -1yD2 = 0 3dy + 0 = 2 + e5x + -2y + -1yD2 3dy = 2 + e5x + -2y + -1yD2 Divide each side by '3y'. d = 0.6666666667y-1 + 0.3333333333e5xy-1 + -0.6666666667 + -0.3333333333D2 Simplifying d = 0.6666666667y-1 + 0.3333333333e5xy-1 + -0.6666666667 + -0.3333333333D2 Reorder the terms: d = -0.6666666667 + -0.3333333333D2 + 0.3333333333e5xy-1 + 0.6666666667y-1
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