1. By showing the steps of proving, determine the type of equation for the following differential cquation. dy xy dx x +y a) b) (e* sin 2y)dx+(e cos 2y)dy = 0 dy 6cx-6xy, where c is constant. dx c) %3D

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

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Q: dy + y tan x = e2x cos x dx „y(0) = 2

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Q: Given y = f(u) and u = g(x), find dy dx y = tan u, u = 11x-4 = f'(g(x))g'(x) = dy -= f'(g(x))g'(x)…

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Q: dx dy y²+x² 3x²y+y³+2xy

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: 7 Sin (3x) Sin (5x) dx

A: The objective is to evaluate the integral ∫0xsin(3x)sin(5x)dx Use the trigonometry formula:…

Q: Find the differential dy of the given function. (Use "dx" for dx.) 7 y = 6√x + 7 x dy = (3x72xx)dx…

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Q: |( + 3t) sin(2t) dt 13.

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Q: d y 4. dx3 d-y + 5xy = 0 dx² + sin x

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Q: Differential Calculus:

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Q: 1. Linearize each function about the indicated xo and express your answer in the form y a yo + m (x…

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Q: the non homogemesus. equation Salve メ++5 2x +24+7 ot x

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Q: If x²y" + xy' +(x? -v-0 x>0,V=x sinx and y=y,v. Which of the following equations satisfied by v…

A: Explanation of the solution is given below...

Q: II. Find dy/dx of the following functions: 1. y = cosh √√4x²+3 2. y= sec hx² x² +1 3. y=xcsche4x

A: See this solution in below

Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

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Q: Compute the differential dz of the function. z = a°!l 9,,11 dz

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Q: dx √₁²x²+² x²+2x+10 dx using Gauss-Legendre and Gauss-Chebyshev Quadrature formulae. 6. a) Evaluate…

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Q: dy 4) Find by implicit differentiation, where dx y5 + x²y° = x* + y.

A: The objective is to find dy/dx by implicit differentiation

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.