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please send complete step by step handwritten solution Q

(a) Find the general solution of the the second-order linear ODE \[ 2 y^{\prime \prime}-5 y^{\prime}-3 y=0 . \] (b) Find the general solution of the inhomogeneous second-order linear ODE \[ 2 y^{\prime \prime}-5 y^{\prime}-3 y=10 \sin x . \] (c) Find the solution to the Initial Value Problem \[ 2 y^{\prime \prime}-5 y^{\prime}-3 y=10 \sin x, \quad y(0)=4, \quad y^{\prime}(0)=1 \]