SOLUTIONS OF DIFFERENTIAL EQUATIONS 2.53. Check whether each differential equation has the indicated solution. Determine which...

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SOLUTIONS OF DIFFERENTIAL EQUATIONS 2.53. Check whether each differential equation has the indicated solution. Determine which solutions are general solutions. 2.54. (a) y" - 2y + y = x; y = (c₁+c₂x) ez + x + 2 (b) tI'(t) + I(t) = 1²; t33tI= c y = xy' + √'; 27x¹ + 256y = 0 d'V d²V +8 + 16V = 0; V=c, sin 2t + c₂ cos 2t + cat sin 2t + cat cos 2t dts dt2 (d) (a) Show L SOLUTIONS OF DIFFERENTIAL EQUATIONS 2.53. Check whether each differential equation has the indicated solution. Determine which solutions are general solutions. 2.54. (a) y" - 2y + y = x; y = (c₁+c₂x) ez + x + 2 (b) tI'(t) + I(t) = 1²; t33tI= c y = xy' + √'; 27x¹ + 256y = 0 d'V d²V +8 + 16V = 0; V=c, sin 2t + c₂ cos 2t + cat sin 2t + cat cos 2t dts dt2 (d) (a) Show L