Home /
Expert Answers /
Calculus /
b-find-the-general-solution-of-the-inhomogeneous-second-order-linear-ode-pa711

???????

(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 \[ 2 y^{\prime \prime}-5 y^{\prime}-3 y=10 \sin x, \quad y(0)=4, \quad y^{\prime}(0)=\mid 1 . \]

Solution: (b) The auxiliary equation of the given differential equation is 2m2-5m-3=0 ?(2m+1)(m-3)=0 ?m=3 and m=-1/2 Thus, the complementary function