Solve the initial value problem. dy + y sin x = 2x cos² x, dx y(0) = 0 COS X - 2.

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

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Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: Cos X- cosy Jax-sinxsiny dy=2

A: A differential equation of the form Mdx+Ndy=0 called exact differential equation if ∂M∂y=∂N∂x and…

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

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Q: Solve for the particular solution of y' = 1/1 e 42 +3 sin 2x when x = 0 and y = 1

A: The differential equation is given by y' = 12e4x+3sin2x The initial condition is  y0 = 1 To…

Q: (sinxy +xy cos xy) dx + x² cosx y d y = о

A: The solution is given as

Q: If y = cos¹ (v₁²), X = find dz? 1 Vu² +1 2= ln (2x-3y)

A: Consider the given equations, y=cos-1vu2x=1vu2+1z=ln2x-3y here we need to find the value of dz.…

Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

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Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: 37/2 8 cos x dx T/2

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Q: y" – 2y" + 3y' = x² + cos3x

A: Answer

Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: Solve dy dx + y tan x = -y³x sec²(x)

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Q: [5/4 sin x dy dx

A: Here we have to find the double integral.

Q: TT/2 S,"/e cos?x.sint x dx in tegralinin bulunvz sonucunu

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Q: dx 6. [- xIn x sin 5tdt 7. V1+ cos 5t

A: Given that the integral ∫dxxln2x. Give suitable substitution to simplify the integral. Let u=lnx,…

Q: Solve the following equation for y(x): y" + 4y = 6 cos 3x + 20 sin 3x

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Q: N/7 2. 4 cos x dx 3+2 sin x 9.

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Q: •π/2 (cos x - sin x) dx

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Q: dx J5+4 cos2 x CO

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Q: Q: Classify and Solve dy sin x dx sin x sin 2x +y cos x

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Q: 9. Solve the equation for 0 < x S 2n: sinx + cosx = 0 10. Solve the equation for 0sxS 2n: sec?x +…

A: Given that: 9. sinx + cosx =010. sec2x+2secx=0

Q: x3 Vx-5 у сos x. sin?x cos3x - Find dy/dx of

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Q: IV. 4x + 2 dx x² + x + 5 V. 2x – 1 dx x² – 7x + 10 VI. | sin(3x) cos(5x) dr

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Q: Find the first two positive solutions to 2 sin(3t) 1 t -

A: We have to find first two positive solutions to given equation.

Q: 7/2 SAT sin" x cos3 x dx

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Q: ㅠ (2 cos x - 2 sin x) dx

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Q: - y = 1 Solve %3D O a. y = tan(x + k) O b. y = sin(x + k) O c. y = cos(x + k) O d. y = e + k

A: Explanation of the answer is as follows

Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

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Q: g. cOS x Vsin x dx

A: Let sinx = t