(10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

Q: Sze*2dx = 1. This is a difficult integral to compute by standard methods (there's a neat trick…

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Q: Solve X x (t) = y(t) = - 17 ²7] [7] (0) - x (0) = 4, y(0) = 19

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Q: Given that g(2)=4 and g'(2)=3, what is the value of h'(2) for the function h(x) = eg(z), 7e? 3e? 3e4

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Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: Let h(x) = f(x)g(æ). If f(x) = –3x² + 2æ – 3 and g(x) = -322 + 4x + 3, what is h' (1)? %3| Do not…

A: Given function is h(x)=f(x)g(x) where f(x)=-3x2+2x-3 , g(x)=-3x2+4x+3 f(1)=-3(1)2+2(1)-3=-3+2-3=-4…

Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

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Q: Solve for y(x): [y(x)³¹(x) = e³(x) y(0) = i

A: Given Differential Equation

Q: (2) Solve for y in terms of x In (2y+1) + 3x = 1n (4) -1 given

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Q: Use the convolution to write a formula for problem: y" + 25y = f(t), y(0) = -2, y(0) = 1. |

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Q: 7. Find the value of h(2) given that (ho gXx)= 4x +4x+4 and g(x) =2x + 1.

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Q: Given that f(z) = 9z- 3 and g(x) = 6 – a', calculate (a) f(g(0))– |3D (b) g(f(0))=

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Q: (c) J2 +∞ dx 2 x ln² r

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Q: Find (f-¹)'(-6) given the following table of values. (Enter an exact answer.) Provide your answer…

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Q: (b) Solve y" +y - 6y = e2t.

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Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

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Q: 8. Given the function h(x)=Vx² - 4 +Vx+2, find h(2), h(0), and h(-x).

A: h(x) is given. We have to find h(2), h(0) and h(-x)

Q: Solve the following edo y²dx + (x² + xy + y²)dy = 0, y(0) = 1

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Q: 6x 24x - 6x is g'(x) = * is R'(w) = 4. The derivative of g(x) (2-x)2 4w5+4w3-6w²+3 2-x 5. The…

A: 4) Given:       gx=6x22-x      g'x=6·ddxx22-x                =6·ddxx2·2-x-x2·ddx2-x2-x2…

Q: e + xy + 4x = 1 ise y"(0) =?

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Q: Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(‡)=C − x y O arctan (=) = C - x² - y²…

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Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67

Q: (b) If 38 10z f (2) = (2** + 6) e then at how many points the function f (z) is not differentiable?

A: f is every where differentiable, there are no points such that the function f(z) is not…

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.