In Problems 31 through 42, verify that the given differential equation is exact; then solve it. 38. (x + tan¬1 y) dx + x +y 1+ y2 dy = 0

Q: 41. y' + (1/t)y= 3 cos 2t, t> 0

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Q: Each of the differential equations in Problems 31 through 36 is of two different types considered in…

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Q: 11. (y² + 1) dx = y sec² x dy

A: Solution of differential equation is following : -

Q: a. Solve the following Initial value problem: xcos²(y)dx + tan y dy = 0, y(2) = 4 b. Give two…

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Q: If the following differential equation is exact, select the solution to the initial value problem…

A: We have to find solution

Q: The complementary solution to the differential equation dy + (2x + 1)y = e da is of the form Yc…

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Q: In each of Problems 10 through 11, determine the values of r for wh differential equation has…

A: Here we have,  10) y''+y'-6y=011) y'''-3y''+2y'=0

Q: (x + y - 4)dx - (3x - y - 4)dy = 0; whenx = 4, y = 1

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Q: Given the differential equation y'-y=3 and the initial condition y(0)=a, what is the value of a that…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Each of the differential equations in Problems 31 through 36 is of two different types considered in…

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Q: A. In each of Problems 1 through 10, solve the given equations using exact differential equations.…

A: Given: 1-xy-2dx+y2+x21-xy-2dy=0

Q: Find the General Solution of the given exact differential equation. dy (8x + 7) + 2y= x da

A: We have to find the general solution of the given differential equation

Q: In Problems 17 through 26 given differential equation. stant C so that y(x) satisfie computer or…

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

Q: 1) Find the general solution to the following differential equation. dy +y (cotx) = 5e* dx %3D

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Q: 4. The particular solution (x = 1, y = 0) of the differential equation X+x cos -y sin dx + x sin dy…

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Q: In each of Problems 21 through 24, determine the values of r for which the given differential…

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Q: 1. Solve for the general solution of the given differential equation. (x – ylny + ylnx)dx + x(lny –…

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Q: 1. Find the order and degree of the differential equation: dy +5 dx 4 14 sin x. dxº

A: Given- d9ydx9+5dydx4=14sinx To find- order and degree of given differential equation

Q: If the following differential equation is exact, select the solution to the initial value problem…

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Q: 7. yy' = (x + xy²)e²²

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Q: 1. (ex + lny + 7) dx + ( 85 + In x + siny) dy = 0

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Q: In each of Problems 14 and 15, determine the values of r for which the given differential equation…

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Q: Given the differential equation y' = e (2x –4) and the initial condition y(5) = a what is the value…

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Q: 3. (a) Solve the given differential equation y" + 4y = (x² – 3) sin 2.r. (b) Without solving. What…

A: (a) Consider the given equation, y''+4y=x3-3sin2x First find the complimentary function. Write the…

Q: B. In each of Problems 5 through 9, verify that each given function is a solution of the…

A: We have to verify that the given function is a solution to the differential equation if it is the…

Q: In Problems 31 – 36 solve the given differential equation by finding, as in Example 4, an…

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Q: A. In each of Problems 1 through 3. verify that each given function is a solution of the…

A: Given- The differential equation y"+2y'+y=0 To check-  whether the solution of the above…

Q: -. (ex. + Iny + 2) dx + +In+siny) dy = 0 sin y)

A: To solve the given differential equation

Q: 11. d = 4√xy dy dz

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Q: 1 Determine the form of the general solution to the following differential equations d. y3) + y" +…

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Q: In each of Problems 10 through 11, determine the values of r for which the given differential…

A: Please refer to the image below

Q: In each of Problems 21 through 24, determine the values of r for which the given differential…

A: Given y"+y'-6y=0

Q: B. In each of Problems 5 through 9, verify that each given function is a solution of the…

A: The given differential equation is y''+2y'-3y=0. Substitute yt=e-3t in y''+2y'-3y=0 and obtain that,…

Q: In each of Problems 13 through 20, verify that each given function is a solution of the differential…

A: The given differential equation is y''-y=0 The objective is to verify that y1(t)=et, y2(t)=cos ht…

Q: A. In each of Problems 1 through 3. verifv that each given function is a solution of the…

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Q: C. In each of Problems 10 through 11, determine the values of r for which the given differential…

A: The given differential equation is y'''-3y''+2y'=0. Substitute y=ert in the above equation and…

Q: dy 8. dx cos 2x; y(0) = 1 dy 10. — хе xe-*; y(0) = 1 dx

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Q: Consider the following initial value problem. dy 2xe + (x2e – sin(y))- dx y(0) = 1/3 (a) Determine…

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Q: In each of Problems 19 through 21, verify that the functions y1 and y2 are solutions of the given…

A: The given system is, y''+4y=0,y1(t)=cos2t,y2(t)=sin2t. Write the homogeneous solution.…

Q: 17. 2t²y" + 3ty' — y=0, t>0; y₁(t) = t¹/², y₂(t) = t-¹

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Q: In problems 1 to 3 solve the given differential equations by writing the general solution. Write all…

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Q: dy 3. dx + y = 2xy² ex

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Q: In Problems 1 through 12, verify by substinution that each given function is a solution of the given…

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Q: In Problems 1–22 solve the given differential equation. 15. Зx?у" + 6ху'+у%3D0

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Q: B. In each of Problems 5 through 9, verify that each given function is a solution of the…

A: According to power rule of differentiation ddxxn=nxn-1 . Now differentiate the function y(t)=t3 once…

Q: In each of Problems 38 through 42, a differential equation and one solution yı are given. Use the…

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Q: In each of Problems 25 and 26, determine the values of r for which the given differential equation…

A: Given differential equation is t2y''+4ty'+2y=0         (1) Also given that  y=tr is the form of…

Q: In each of Problems 11 through 14, find and plot both the steady periodic solution xsp(t) = C cos(@t…

A: 11. Given,              x''+4x'+5x=10cos3t;    x(0)=x'(0)=0

Q: In Problems 1 through 10, find a function y = f(x) satisfy- ing the given differential equation and…

A: Given that a differential equation and solve and find y value . And also given that a condition…

Q: 9. dy 在 2 1+y²

A: Sol