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(Solved): problem 3  Find the general solution of the following differential equations (complementary fun ...



problem 3 

Find the general solution of the following differential equations (complementary function + particular solution). Find the pa
Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23), or (6.24). Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after \( (6.15)] \). 1. \( y^{\prime \prime}-4 y=10 \) 2. \( (D-2)^{2} y=16 \) 3. \( y^{\prime \prime}+y^{\prime}-2 y=e^{2 x} \) 4. \( (D+1)(D-3) y=24 e^{-3 x} \) 5. \( \left(D^{2}+1\right) y=2 e^{x} \) 6. \( y^{\prime \prime}+6 y^{\prime}+9 y=12 e^{-x} \) 7. \( y^{\prime \prime}-y^{\prime}-2 y=3 e^{2 x} \) 8. \( y^{\prime \prime}-16 y=40 e^{4 x} \)


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