(Solved): For each of the FOUR 2nd-order linear, non-homogeneous ODE with constant coefficients listed at the ...

For each of the FOUR 2nd-order linear, non-homogeneous ODE with constant coefficients listed at the bottom of the problem, from below options, selec he correct form of a particular solution \( y_{p} \). A. \( y_{p}(x)=A x^{2}+B x+C \), B. \( y_{p}(x)=A e^{2 x} \), c. \( y_{p}(x)=A \cos 2 x+B \sin 2 x \), D. \( y_{p}(x)=(A x+B) \cos 2 x+(C x+D) \sin 2 x \) E. \( y_{p}(x)=A x e^{2 x} \), F. \( y_{p}(x)=e^{3 x}(A \cos 2 x+B \sin 2 x) \) For each ODE, enter your choice in the box. 1. \( \frac{d^{2} y}{d x^{2}}-5 \frac{d y}{d x}+6 y=e^{2 x} \) 2. \( \frac{d^{2} y}{d x^{2}}+4 y=-3 x^{2}+2 x+3 \) 3. \( y^{\prime \prime}+4 y^{\prime}+20 y=-3 \sin 2 x \) 4. \( \quad y^{\prime \prime}-2 y^{\prime}-15 y=e^{\prime \prime} \cos 2 x \)