Solve the system Sa' (t) = x(t) + y(t) ly(t) = y(t) Then what is æ(t)? O x(t) = 2(0)e O a(t) = 2(0)e' + y(0)te O x(t) = x(0)e' + x(0)te'

Q: ' (x² +2)+4x(y² +2y+1)=0, y(0) =1.

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Q: Solve 4 2 M-[30 Ly'. -26 -8 x (0) = -2, y(0) = 22

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Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

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Q: Use separation of variables to solved = e* (1 - y)², given y(0) = 0 Oy=-(e² - 1) + Oy=1-e-* Oy =…

A: Given differential equation dydx = ex( 1 - y )2 y( 0 ) = 0

Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: If r(y) = e³y² +3 find r'(y) =

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Q: c'(x) = e(x) e'(x) = t(x) t'(x) = h(x) h'(x) = c(x) 0 1 2 1 0 4 3 3 4 1 2 لا e(x) c(x) 3 t(x) 4 1 3…

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Q: Take the system Find a particular solution of the form *₁(t) = x₂ (t) = help (formulas) = v cos(4t)…

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Q: 61. u = cos(x²y)

A: 61. The given function u=cosx2y. We have to verify that uxy=uyx.

Q: If f(t)= et and g(t) = 5t² - 2, use the chain rule to find the derivative of y = f(g(t)). y =…

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Q: x A(x) = † (3-1²) dt 0

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Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: 3 ve the nonhomogeneous system tY' = (²2 =²) x + (-²₁) -21). Y (2-2)

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Q: If y = f(x) is the solution of y" – 9y" +26y' – 24y = 0, f(0) = 4, f'(0) = 15, f" (0) = 44, then

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