H.W.1 Solve the initial value problem y" + y' + 0.25y = 0. MO) = 3.0. y'(0) =- -3.5. y = (3 - 21)e-0.5, Answer H.W.2

Q: Find to 2 decimal places the solutions to the equations a. ex-2 = 10 b. ln(4t + 1) = 1 + ln(3t - 2)

A: The given equations, a) ex-2=10 b) ln4t+1=1+ln3t-2. We have to find the solutions to the given…

Q: e' ? Explain. 1. Is X = te' a solution of X'=

A: Given: X=11et+1-1tet and X' = 2134X+-17et. To check: X=11et+1-1tet is solution of X' = 2134X+-17et

Q: 23. If mDH= (1lx + 7), mGF= (5x + 9)", and M2GEF = (10x – 22)', find mDH %3D 5x+9=10x-22 H. mDH=

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Q: Question 3. Solve the IVP x" + 2x' + 2x = 0. when x(0) = 0, x' (0) = 1

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Q: Use boundary conditions (2) in u (x, 1) = X (t) T (1) are, u (0, t) = X (0) T (t)=0 And u (L, t) = X…

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Q: 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in…

A: The growth rate of a colony of ants is given by 10t/(1+t2)2 Initially there are 100 ants ∴ Number of…

Q: Do the ordered pairs (x, ln(y)) form a linear or exponential function? Justify your answer. e. Find…

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Q: 1.2y" - 5y' - 3y = 0

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Q: Find the given derivative. DX 5x -- Dx 5x 1/3 1/3

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Q: 2x + k The equation of a curve is given by y = (T dx. x+1 It is given that the curve has a turning…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.