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![Solve the given initial-value problem.
\[
2 y^{\prime \prime}+3 y^{\prime}-2 y=10 x^{2}-8 x-13, y(0)=0, y^{\prime}(0)=0
\]
\[](https://media.cheggcdn.com/study/fc6/fc61e540-c6b3-429f-9033-21f50fe90fed/image)
Expert Answer
Given the Initial value problem 2y?+3y??2y=10x2?8x?13, y(0)=0,y?(0)=0we first find the general solution of the homogeneous equation:2y?+3y??2y=0The