dx -(I+ 2x tany) ay co

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

A:

Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

A:

Q: y = C,e²x cos(3x) + C2e2x sin(3x)

A: y=c1e2xcos3x+c2e2xsin3x  differentiate with respect to x…

Q: dx dy -2xcsc 2y - 2x³ cos 2y sec 2y x² = sin 4y + (4y + C)2y

A:

Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

A:

Q: d²y Find 2 dx? y = sin 2x+cos² x

A: Using derivatives.

Q: sin(x²-1)y separable or not dy dx y2-1

A: To find given differential equation is separable or not .

Q: y' + 2y = 3 sin(e2×)

A: y.e^(2x)=-3/2 cos(e^(2x)) + k

Q: J cos 3x cos 4x dx :

A:

Q: D- y" + 2y' + 5y = 6e2* + x sin? x + e*cos 2x %3D

A:

Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

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Q: dy/dx= 4 cos 4x

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Q: y= cos (1-t) and x=V2t - t2

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Q: *10. cos Z = 0.5234 YX _ y 24

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Q: z = cos(10xy) %3D dz %3D

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Q: Take the derivative of this integral.

A: Given

Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

A:

Q: BERNOULL니 dx -X = x siny dy ANSWER; hus -) § losy + Ce) X= -

A: dxdy-x=x3/2sinyx-3/2dxdy-x-1/2=siny                        1 Substituting x-1/2=v…

Q: 5-2x dy if y = cos Find dx %3D 5+ 2x

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

A:

Q: (y − cos²x) dx + cos x dy = 0

A: To solve the differential equation: y-cos2 xdx + cos x dy=0 Let us simplify this, y-cos2 xdx + cos x…

Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: 1 and y' CO)

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Q: cos e de =_ %3D • 2 • -T • 6

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2-+x* cos y = 0 dy y

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Q: cos³ 4y /sin 4y dy

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Q: Find d²y/dx² implicitly in terms of x and y. 4xy 5 cos(x) = -9 d²y dx² || X

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Q: 5. (y" – y) = e-X cos(3x) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (一 - dx t - 3 X*cos(3)-4-2 ) -)dy=0 = 0

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Q: 2 dx (a) t = tan x. %3D 5+4 cos 2x 0.

A:

Q: dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

A: The given initial value problem is: dxdt+3x=cos(5t) ;         x(0)=1

Q: x cos x² 2. X C0 dx -siny

A:

Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: +3x2, (V)² = sin³(cos³(*3**» dy b. Find dx %3D

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Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

A:

Q: 6. J1-cos I COS T dx

A: Answer is mentioned below

Q: (c) So cos(-x)(x²)dx (d) S(3x² – 2x + 1)sin dx

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Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: dy x- y = x.cos² ² 1- dx

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: b- y" -y+2y+ cos x, 05x y(0) -0.3, y()--0.1

A: To show the boundary value problem has unique solution we solve the given ode by method of…

Q: (2xsinx +3 cos y)dx-3x sin ydy 03 ....

A:

Q: Differentiate

A: Derivative of a function is the rate of change of the function. It gives the slope of the function…

Q: dx 2- Find dy of y = /cos-1(In (xy)) y %3D

A: Given: - The function is, y=cos-1(ln(xy))xy To find: - The derivative of the function, dxdy

Q: Find the solution of d2y/dx2+4y=sin3x+cos2x

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Q: X cos (3x) dx,

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Q: Evaluate the dy/dx> d) y=e-x((cos(2x)) a) -e-x(cos2x+2sin2x) b) e-x(sin2x-cos2x) c)…

A: y=e-xcos(2x)differentiate…

Q: Find the solution of dx - (1+2x tany) dy = 0

A: Given: dx-1+2xtanydy=0

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.