Solve the differential equation in Exercises 9–22. dy dy = x²Vy, y> 0 10. dx 9. 2Vxy = 1, x, y > 0 dx dy 11. dx dy 3x e 12. dx dy dy 13. Vycos? Vy dx 14. V2ry dx dy = ev+sin x dx dy 15. Vx dx x > 0 16. (sec x)- dy 2rV1 – y², -1< y < 1 17. dx dy 18. dx e2r-y er+y dy 19. y? Зx2уз —бх? dx dy 20. — ху + 3x — 2у — 6 dx 1 dy х dx dy 22. dx ye + 2Vye 21. et-y + e* + e¯y + 1 %3D

Q: Solve the differential equation d?y dy 3 + 2y – t = 0 dt dt2 subject to the initial conditions that…

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Q: Verify that the indicated family of functions is a solution of the given differential equation.…

A: A family of functions y1 is said to be a solution of the differential equation if it satisfies the…

Q: Verify that the indicated family of functions is a solution of the given differential equation.…

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Q: determine the differential equation of the family of lines passing through the origin. x dy - y…

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Q: Form the differential equation for the function y = a sin3x -bcos3x O a. y" - 9y 0 O b. 9y" + y = 0…

A: Given differential equation is: y=asin3x-bcos3x                                                (1)…

Q: Solve the differential equation: 2cos(2x)y^2+2ysin(2x) dy/dx = 0, y( π/8 ) = −2, find y(t)…

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Q: Evaluate the differential equations: Integrating Factor by Formula a) (2y2 + 2y + 4x2)dx + (2xy +…

A: Given:  a) 2y2+2y+4x2dx+2xy+xdy=0b) y2cosxdx+4+5ysinxdy=0

Q: Solve the differential equation, 2ydy = (3y? cot r +sin rcosr) da sin z- sin 3* y² = C %3D csc z csc…

A: We will find out the required solution

Q: Exercise 2.7 dy 2cosx-sin². -sin x+ y 1. Verify that y, = sinx is a solution to and solve the %3D…

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: The solution of the differential equation is dy Y =sin x dx x O x(y +cos x ) = sin x +c O x(y - sin…

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Q: Solve the differential equation. dy = 3x?ey dx O y = In (3x3 + C) O y = C In (x) O y = In (x3 + C)…

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Q: Find the order differential equation of ddy] 6 dy dy dy +7. + 6- 3. +7 = 0 dx3 dx2 dx

A: Given that a differential equation and find the order of this differential equation. We know that…

Q: Consider the differential equation (3ze" + 2y)dz + (z²ev + z)dy = 0, z>0. Verify that the equation…

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Q: test whether the differential equations are exact and solve those that are. 2Y dy 0 dt+-

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Q: Solve the differential equation. dz + 4et + z = 0 dt %3D - In(#|) z = C+

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Q: Find a linear operating point model of the differential equation: d²x dx + 3 + 2x = sin x dt2 dt a)…

A: Consider the provided question, Given D.E, d2xdt2+3dxdt+2x=sinx We need to find a linear operating…

Q: Determine the solution of the differential equation y" – 2y' + y = %3D - 1+x2 y = C,ex + C2xe* +÷e*…

A: This is non homogeneous equation of second order so using the method of variation of parameter we…

Q: Solve the differential equation: Cos(x) dx + ( sin(x+y) + sin(x- y))dy=0 Hint: sin (A + B) =sin A…

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Q: Linearize the following differential equation about point, x= T/3. d²x +2 dt? dx + sin x=0 dt

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Q: Solve the differential equation, 2ydy = (3y² cot r +sin xcos1) dr %3D sin z sin 3* y? = C O csc z…

A: We will find out the required solution.

Q: Evaluate the differential equation dy/dx = 3/x. a. y = In 3x + C b. 3y = In x + C c. e = In x³ + c…

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Q: In Exercises 33–36, solve the given differential equations (a) by varia- tion of parameters and (b)…

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Q: Solve the Euler-Cauchy differential equation x2. dx? d’y 2x+5y = In? x- Inx. dy +5y = In² x– In x.…

A: Consider the provided differential equation,

Q: Solve the differential equation: Cos(x)dx + ( sin(x+y) + sin(x– y))dy=0 Hint: sin (A ± B) =sin A cos…

A: Given differential equation  cos(x) dx + {sin(x+y) + sin(x-y)}dy    Using identity of sin(x+y) and…

Q: dy dy -4 =0 dx dx O 2 and 6 O 2 and 4 O 1 and 6 O 1 and 4

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Q: Convert the differential equation d²y - 3y + 2y = 4 sin x dx² dx with the initial conditions y(0) =…

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Q: Determine the solution of the differential equation y" + y = sec² а. y = C, cos x + C2 sin x – cos x…

A: The given differential equation is; y" +y'=sec2x

Q: solve the differential equation. 3y(x + 1)? In Exercises dy dx Vy cos Vy 31. 32. у 3 y - 1

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Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: The solution is given as

Q: A) Solve the Differential Equation (e +In y+) dx+ (+ In x+ sin y )dy 0 %3D

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Q: Determine whether the family of functions x = c, sin t + c2 cos t is a solution of the differential…

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Q: Determine the differential equation of the family of lines passing through (h, k). A. (y- k) dx -…

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Q: To reduce the differential equation with linear coefficients (x+2y- 4)dx– (2x+ y- 5)dy= 0 to a DE…

A: We have to convert given differential equation into dydx=f(x,y)  form and then find proper…

Q: Solve the linear differential equations d²x +2+ 0,x = 0, = dx + 5x = 8et when t = dt dx = 8 dt dt2

A: This question is related to solutions of differential equation.

Q: Is the differential equation (uv+u)du = [(u^2)*(v^2) + u^2 + v^2 + 1]dv separable?

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Q: / Solve three of the differential equations below: dy А. secx dx ev+sinx %3D B. (2y sinx - cos y) dx…

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

Q: To reduce the differential equation with linear coefficients (X+2y-4)dx - (2x+y-5)dy=D0 to a DE with…

A: We are going to solve

Q: Transform the equation y' differential equation. O (1 + x²) dx - dy = 0 O (1 + x²) dx 2x 0₁dx 1 + x²…

A: y'=2xy1+x2

Q: Solve the differential equation: (9 + 2x sin y) dx x? cos y dy = 0 O z sin y = ca – 3 O (E) O z +…

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Q: ifferential equation: dy/dx=(y(y cosx+1))/(y sinx+2x-2y) Condition: y(0)=-1

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Q: Evaluate and solve the linear differential equation. (d2x)/(dt2) + 2 (dx)/(dt) + 5x = 8e-t, when t…

A: Given differential equation can be writen as, (D2+2D+5)x=8e-t.....(i)d=ddt,…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy = (8x…

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Q: Convert the equation d°y dy -3 x y 0 dx3 -3. and initial conditions y(0)= 1.11983, y'(0)=0.83697 and…

A: Introduction: A higher order linear differential equation can be converted into a system of first…

Q: Determine the differential equation whose integrating factor is x2 A (2у-3x) dx + х dy%3D0 B В y dx…

A: Suppose we have the first order differential equation dydx+Py=Q,where P and Q are…

Q: Verify that the indicated family of functions is a solution of the given differential equation.…

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Q: Form the differential equation for the function xy ax2 + 2bx-c O a. xy" + 3y" 0 O b. xy" - y" 0 O c.…

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Q: Solve the differential equation. dy = 3 cos x sec y dx Oy = sin1 (3 sin x + C) O y= sin (3 sin x +…

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Q: solve the differential equation by the Laplace: 2- y" + y = 16 cos t y(0) = 0, y'(0) = 0

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Q: Solve the differential equation as shown below; dy = [rosytan 1 cosx Lcotytanx dx cosy A siny?=…

A: For the solution of the problem follow the next steps.

Q: In Exercises 31–34, solve the differential equation. Зу(х + 1)? dy 31. Vy cos? Vy dx 32. y' y – 1…

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