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Math  /  Calculus

Question2) Solve the initial-value problem 2y′′+y=4δ(t−π);y(0)=0,y′(0)=12 y^{\prime \prime}+y=4 \delta(t-\pi) ; \quad y(0)=0, y^{\prime}(0)=1
HINT: Use the example we discussed in class from section 6.5 as a guide.

Studdy Solution
Our solution to the initial-value problem is: y(t)=2sin⁡(t2)+22uπ(t)sin⁡(t−π2) y(t) = \sqrt{2}\sin(\frac{t}{\sqrt{2}}) + 2\sqrt{2}u_\pi(t)\sin(\frac{t-\pi}{\sqrt{2}})

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