Solve the following DE: [3sin (y) — 5x ]dx + 2x²cot(y) dy=0 Ox²[sin (y) - 2x]³=C'sin³(y) Oy³[sin(y) +x]²=Csin³(y) Oy³[sin(y) + x²]²=Csin(y) Ox³[sin(y)-x]²=Csin²(y)

Q: If r(2) = sin(z² – 10z + 16), find r' (z) =

A: Since, we have been given that r(z)= sin(z2-10z+16)Our Aim is to find r'(z)=?

Q: 5 Find y' if cos (Xty) =

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Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

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Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: Find one solution of y" + 2y' - 2y = 3e³* cos(2x).

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Q: 6. Find Sin 5x (b) y = THcos 5x dx

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Q: dy (=)y = x* sin x. dx

A: Linear differential equation

Q: 3. Use the following functions of x E R' to answer the rest of this question: 1 f(x) 1 =; 9(x) = ;…

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Q: Solve: [xcos² (y/x) − y]dx + xdy = 0 4lnx + sin(2y/x) = C 2y 4lnx + sin(2y/x) = C x sin(2y/x) = C +…

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Q: sin(y)dx + cos(y)dy = 0 by exact

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Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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Q: Find the general solution:

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Q: Q-7. Solve the differential equation y = 1+ fip +..... for | 1 |< 1. dz dz

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: (i). y' = 1 + 3y tanx Ans. 3y cos³x = c + 3sinx - sin³x

A: this is a linear differential equation. solve it using integrating factors.

Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. (A) cos y sin x =C sin y B…

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Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: SHOW WHETHER THE FOLLOWING DE IS EXACT OR NOT 1. (y^2 – 2x)dx + (2xy + 1)dy = 0 2. x[1 – sin(y)]dy =…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: 3 x* cos(3 y) 2 x³ sin(3 y) dx + + 2 x2 ) dy = 0

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Q: (1+x)y' + y = cosx; y(0) = 1

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Q: y=(b+x²)* +(1+x³)*(/3x² +x – c)cos²(4x) y' =?

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Q: find dy/dx of the following:

A: Please refer to the image below

Q: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

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Q: 2/x?y" – 2xy' + 2y = x³ cos x

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Q: - (2xy - sin x) dx + (x² − cos y) dy = 0

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Q: S cos 4x cos 3x dx

A: Given: I=∫cos(4x)cos(3x)dx