d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos 3x-2 sin 3x] 12 3

Q: Find the general solution of the differential cquations : d2y = e2* (12 cos 3x – 5 sin 3x) dx2 2.…

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Q: the general solution of the DE (cosxcosy+2x)dx-(sinxsiny+2y)dy=0 is

A: The differential equation M (x, y) dx + N (x, y) dy = 0 is exact if and only if  ∂M∂y=∂N∂x.   The…

Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

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Q: 15. Solve d²y +3 y + 2y = 3 sin x, given that when x 0, y =-0-9 Wor, OFer dx? dx dy =-0-7. dx and…

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Q: Show that an implicit solution of 2x sin2(y) dx – (x² + 11) cos(y) dy = 0 is given by In(x² + 11) +…

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Q: 1. S (5x-12) dx 2. S x³-6x² +8x 3. S -(3 cos² 0 +8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0 dx…

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Q: dy Q3) Find dx y = (cosx)v2 y = 3tanx In3 2 - e = ylnx 4 - y = cot-1! 1- 3 - + tan-1x 5 - y = =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4. (ye"-2y)dx + (xe-6 xy- 2y)dy = 0; x = 0 when y = 2. 5. (x+3) cos y dx - (sin y In(5x + 15)-y} dy…

A: The exact differential equation for the equation, F(x,y)=C, is written as Fxdx+Fydy=0, where, Fx ,…

Q: (cos 2y-3x²y³) dx +(coS 2y -2x sin 2y-2x*y) dy =o 2.[2x + y cos (xy)] dx + x cos (xy)dy=o 3. (xy²+…

A: Using method of exact differential equation.

Q: y' cos x + y sin x = 2cos³x sin x- 1 What is the particular solution when y(T/4)=3v2 ?

A: Given differential equation is y'cosx+ysinx=2cos3xsinx-1 we have to find the particular solution…

Q: 1- xy dy + (x² + y² )dy = 0 dx 2- 2. dy – y = ex/2 3- (x + 2y)dx – xdy = 0 dy 4- cosh x+ (sinh x)y =…

A: As per the guidelines we can solve 2 problems.

Q: Find if y = In x5 + e¯cos2x – lIn e?. dx | dy_5, esin²x-cos²x 4 sinx cos x dy 5 %3D dx e cos²x-sin²x…

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Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: 6. (5x*y+ 4x³y³) dx + (3x³ + 5x*y²) dy = 0 7. 3y4 dx + (4xy³ + 5x¯2y+) dy = 0 8. (2xy? + y + 2xy cos…

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Q: To solve the ordinary differential equation dy +xx dx = sin x, y(0)= 5. 3 by Runge-Kutta 4th order…

A: The form of differential equation to use Runge kutta 4th order method

Q: What differential equation has y = x² cos y- 4x + C as a solution? a. (2x cos y – 4)dy – (1+ x² sin…

A: The solution is given as

Q: 11) (3ycos(3x)dx– sin(3x)dy)/ y = 0 12) sin(ß y)dx =-ß cos(B y)dy

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Q: 1. S 5e* dx 2. S(2 – 3e*) dx 3. S 72x+3 dx 4. S dx x In x 3 dy 5. S 4y-3 6. S dx 2 x+5 7. Se* (1 +…

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Q: Given the differential equation dy 4x2 cos (3y) dx Separate the Variables, and then rewrite using…

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Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x3 + Iny) dy = 0, when x = 0, y = e

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

Q: 22. If y = x+4 then what is 4Y? dx dy a. 4x(x + 4) dy С. dx -4Vx + 8 dx dy b. dx =-4(x + 4)= d. dx…

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Q: 5. (1- xy)-dx + [y2 + x(1-xy)-]dy = 0 6. (y- cos?x)dx + cos x dy = 0

A: Exact differential equation. An ordinary differential equation Mx,ydx+Nx,ydy=0 is said to be an…

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: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: 3tanh 1x 1. S 1-x 2. S cos x dx sin x 1+sin?x e*dx 3. S Vezx-16 4. Find for y = e3* sech x dx x dx…

A: 1. The integral given is  ∫3tanh-1x1-x2dx......................(1) Substitute…

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: The differential equation (3ycosx+ 4.xe* +2x'e" dx+ 3(sin x+1)dy 0 is exact because OM ON Ox

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Q: find (x² – 2x + 1)e²* dx dx 9. 10. fun tan - y dy y dy 11. 12. sin- x sec² x dx 4x sec2 2x dx 13.…

A: Hello thank you for the question. We’ll answer the first question since the exact one wasn’t…

Q: g) y² ex+y = cosh x + √rosh²x -1 +7 et h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy Sin 2x…

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Q: dy 7. Jaye20 sin x dx 8. S 12-cosx 3y²-2y+1 -dy 9.

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Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS

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Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

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Q: dy Find if y = ln x5 + e-cos 2x – In e?. dx dy 5 ,cos?x-sin2 x dy 5 4 sinx cos x = - dx e sin2x-cos2…

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Q: Find the differential equation such that y(x) = (x + 10)°(c,cos(2ln(x+ 10)) +c,sin(2ln(x+ 10))) d²y…

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Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: 3. у(3x3 — х + у)dx + x?(1 — х?)dy 3D 0 4. у(2х — у + 1)dx + x(3х — 4у + 3)dy 3D 0 5. (r + sin 0 –…

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Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: 1. Non-Exact DE (4x² – 4xy + 3y² + 2x – 3y)dx +x(2x – 2y + 1)dy = 0 -

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

Q: cos x + x. d'y y=x° + 72x d'y +y-x" 72x because when tho socond deuvative S substituted for dx he…

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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: 1 If y = sin' x then is dx dy dy -3 cos x b) dx a) –3 sin² x cos x dx sin¯ x dy dy _ -3cosx = -3…

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Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: (sın 2y - 2x cos 2y) dx +( 2x coS 2y + 2xsın 2y)dy=d when x= 2, Y = T 3. COS %3D

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Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: To solve the ordinary differential equation dy 3+5y' sin x, y(0)= 5 dx %3D by Euler's method, you…

A: we have,3dydx+5y2=sinx, y(0)=5

Q: Test for exactness and find the complete solution of dx + [ In 2(x-1) + dy = 0 х-1

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Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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Q: What is the general solution to the differential equation (tan x)dy – (4yIn y – y tan³x)sec?x dx = 0…

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Q: 1. (2xy + x²) dy + (2xy + y²) dx = 0 A2 (3x² + 2xy) dx + (x²) dy = 0 *AA 3. (3x²y³ + 3 sin x + 4y)…

A: Disclaimer: SInce you have asked to solve only question 3, this question has been solved only.…