Question

1. (18) Give the form of the particular solution to be found by the method of undetermined coefficients for the following differential equation. Do not solve. \text { 1) }

y^{\prime \prime}-4 y^{\prime}+4 y=e^{x}+x e^{x}+x^{2} e^{2 x} \text { 2) } y^{\prime \prime}-5 y^{\prime}+6 y=e^{2 x}+x^{2} e^{x} \text { 3) } y^{\prime \prime}+y=e^{x} \sin x+x^{2}

Fig: 1

Fig: 2

Fig: 3

Fig: 4