3X e dx 3x + 3 X e a) S x sin (4x) dx x-y=-1

Q: find dy/dx.1. y = -10x + 3 cos x            2. y = 3/x + 5 sin x3. y = x2 cos x…

A: Given the functions :- 1.  y = -10x + 3 cos x Differentiating with respect to x dydx =…

Q: 10. [x'sin(x')dx 11. [x sin(x)dx 12. [sin(x*)dx 13. ſe* dx 14. [xe* dx 15. [cos (x)dx

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Q: 4. Integrate: 5dx dx a) f b) [ c) f- 1 dx; d) x' V16-x? 1+ cosx cos x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Find the general solution of dy dy dx =sin 2x dx

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Q: 2. Obtain the general solution to the equation dy dx x sin x y cos y

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Q: d [ sin(x)cos(x) dx dx 1+x4

A: Find the integral

Q: 1. S(7x³ + 4x²)dx e*dx 2. J itez* 1+e2x 3. S(V1 – cos x)dx

A: We will these indefinite integrals as

Q: (a) ſ x sin(2+ x²) dx (b) Sí Зи du u²+u–2 (c) ſi z dx 2 x²+x+7 (d) * x²e-3x dx -Зх

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Q: Find the general solution of

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Q: 6x – 2x +1 dy cos y + e4y 2. (3xy² – 9xy – 30x) dx + (x² +9) dy = 0 1. dx

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Q: (1) хdy — ydx — Vx? + у? dx (2) — Зу? — у? sin x dx (3) (x2 + 1)4 — у2 + 1 dy dx

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Q: dx 1. S 2x-x² dy 2. if y = x* (In x)? . dx 3. Sx³e-* dx .

A: We have to find the integration and derivative as asked in the given question.

Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

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Q: xdx g) 7x + 2) h)f sin(In x) dx of xe" dx

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Q: Solve the particular solution of 3y(x^2 - 1)dx +(x^3 + 8y - 3x)dy = 0; when x = 0, y = 1

A: The given differential equation is 3yx2-1dx+x3+8y-3xdy=0. The initial condition is x=0 when y=1. The…

Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

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Q: 1. ſx² e*³ Sx² e**dx 2. cos'xsinxdx sin3xsin 2x dx 3.

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Q: dy 4.x+ (4x² – 1)y = -3 sin(2x) dx dy dx²

A: In this question, we find the normal form of the differential equation and then solve it.

Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e=2x² dx Зdу — 4xу dx

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Q: x + y sin 2 ) dx x sin 2 dy = 0 -

A: The solution is given in the next step.

Q: Using dx/dy solve sin(x+y)-cos(x+y)=1

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Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

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Q: 5. y = l 1- co s x 1+co s x

A: We have to find out dy/dx for given y

Q: zln x dx 2) S 3 cos3 x sinó x dx 3) 12.1 dt 13. 3t + 2

A: Explanation of the answer is as follows

Q: find dy/dx. y = x2 cos x - 2x sin x - 2 cos x

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Q: y2 - cos(x²) + + 3x³ = 4x-3 dy 8. x – %3D dx

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Q: 6. (y cos x + 2xev)dx + (sin x + x²e° + 2)dy = 0; when x = 0, y = 0

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Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

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Q: d²y 10 9y = e3x + sin 3x dx2

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Q: 12) dy dx - = x cos (6x²), y(0) = 7 A) y == sin (u) B) y = sin(6x2) + 12 C) y = sin (6x²) + D) y -…

A: In the question we have to solve the differential equation. Bartleby's guidelines: Please post…

Q: 2. sin y(x + sin y)dx + 2x² cos ydy = 0

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Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

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Q: (2y sin(x) cos(x) – y + 2y e) dx = (x – sin (x) – 4xyey)dy.

A: the differential equation Mdx+Ndy=0 is exact when ∂M∂y=∂N∂x where M and N are functions of x and y…

Q: dx 1. S. 2x-x2 if y = x° (In x)? . dx 3. S x³e-* dx . 2.

A: Note : as per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1- [(2x – 5)/3x – 1) dx | 2- S S(x3 – 10 + 3y² dy dx

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Q: Obtain the general solution of x^2 d2y/dx2 -2xdy/dx+2y=sin(lnx)

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Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

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Q: (メ2メ+Sx )dx h- Cos3x dk 120 x3-XSinx+ CusX dx C. 130 x41 (2メーリdy

A: As per our policy, I can only provide you solution for first three parts, but part (c) is not clear…

Q: dx b) sin 2x sin x dx (3x + 2)²

A: we have to integrate

Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: 3. sin y(x+sin y)dx + 2x² cos ydy = 0 0: uhen v-2

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Q: I sin 2 dy dx (x² – y) dy dx 5. 6. x? – y² dy dx 8. L ellyt dx dy 7.

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Q: 1) ſx e* dx 2) S x³ e* dx 3) ſx² sin x dx

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Q: (1) S(1+ x² ) (2 - x) dx (2) S V? + 4 dx 3) § *³ +2x². dx x* (4) S" 5 e* + 3 sinx dx

A: Note to student : Thanks for posting your queries. But the photo contain multiple questions. As per…

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.