Find the Gcneral Solution of the ff.: * u sing Homogen cous, Exact or Non -Ex act Formula. +) (2xy-tany)dx + (x²- X sec?y) dy = o |2) 2xy dx t (x?+y2) dy = 0

Q: solve the following x cos?y dx+tany dy = 0 -Q1 y dx = ( x+Vy2-x² ) dy -Q2 (sine - 2r cos?e ) dr +r…

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Q: The DE: y =x y+5Vxy is a Bernoulli equation Select one: O True False

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Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

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Q: 7. Find the general solution: ydx + (1 +x?) arctan x dy = 0 a. secx – tan y = c b. arctanx + sin y =…

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Q: Determine the largest interval in which the unique solution of (t-3)y +tan ty t, y(m)=0 is certain…

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Q: Which of the following is the solution of [2x + ycos(xy)]dx +xcos(xy)dy =0 a. x? +cos(xy)=c b. x? -…

A: Given differential equation [2x+ycos(xy)]dx+xcos(xy)dy=0. The objective is to find the solution of…

Q: Which of the following is the form of a particular solution of y" +4y' = 3e2t + cos 2t + t? %3D

A: We have to find the particular solution of given diff equation.

Q: Show if the following statement is true or false. If it is true, write TRUE. If it is false, write…

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Q: B. Prove that the given equation is a solution to the given DE: 5. x= 2t + C; y = Ct + 3 ;…

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Q: Q3) The solution of ODE * (3yx² -) : dx +(x + cosy + dy = 0 O y^2+2x+C O y+y/x+siny+C O y/x+cos x+C…

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Q: Reduce to first order and solve 1> 2xy"= 3y' Cos n ii) xy"+ 2y'+zy = 0, Y, = ニ

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Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: (2) Use appropriate substitution to solve the following 1-1-y dy (i) dr tan (x+ v). (ii) y = %3D z+y…

A: As per our guideline we are supposed to answer only one asked question with first three subparts.…

Q: Given: (2xsinycosy-x+2x2eyx^2)dy=(y-sin2y-4xyeyx^2)dx Show the complete and detailed solution of…

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Q: Determine the largest interval in which the unique solution of (t -3)y +tan ty = t, y(1)=0 is…

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Q: Consider the following first-order ODE: (2xy – sec? x)dx + (x² + 2y)dy = 0 || Solve it using the…

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Q: The equation (tan?x+3y²)sec?xdx+(3tan?x+y²)dy= 0 can be solved by A Bernoulli's Equation B…

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Q: Which of the following is a particular solution Yp to y" + 2y' + 2y = cos /2t

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Q: 3. ® Find the genelal Solution of the differentral egation (D'+ 25) y = cscX Sinx t Sin 5X cos 3X

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Q: . Find the qeueral solution: - 2 dy +5y = ex Cos 2x

A: Complete solution = complementary function + particular integral.

Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: The equation below is said to be 3 dy (x² – 1) \dx, sin x — х - + ye2x+1 %3D O A. Linear and…

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Q: (g) The solution of y' + (2/t)y (cos t)/t², y(7) = 0, t > 0, is Y COS (sin t)/t².

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Q: (cos t)y" + (sin t)y' – ty = 0,

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Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

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Q: Which of the following nonhomogeneous equation cannot be solved the method of undetermined…

A: If the term in the non homogeneous part is of the form eax, sinax, cosax, x,x2,..., xn, then the…

Q: The equation (tan?x+3y?) sec?xdx+(3tan?x+y²)dy=D0 can be solved by A Bernoulli's Equation DE with…

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Q: 2n 37 So² S67 (x sin(y) – y cos(x)) dxdy = %3D

A: The given question can be solved as shown in step 2.

Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

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Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: or the following IVP, determine the t-interval (a, b) on which Theorem 2.1 guarantees a unique…

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Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: Find r(t) for r'(t) = 2/ti + 3 cos(2nt)j – e-'k and the initial condition r(0) =i+2j

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Q: Which of the following equations is NOT an exact equation? (2x sin y + y)dx + (x² cos y + x)dy = 0…

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Q: Determine the form of a particular solution yp for y"+y cosx

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Q: (cos 2y)-3'y de+ [{os 2y)- 2.(sin Zy) - 2xyl dy 0

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Q: a) Find dy/dx and d²y/dx² at the given point without eliminating the parameter x= 0+ cos 0, y=1+ sin…

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Q: Find the solution of sin 3ædx + 2ycos³3xdy = 0 O y? = sec 3xtan 3x + C O y? = -sec 3ætan 3x + C O y?…

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Q: Determine the largest interval in which the unique solution of (t – 3)y +tanty = t, y(n) =0 is |…

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Q: Which of the following equations has solution = = f(cos(x- y)) ? Ob. + 2:, +, =0 , =2:,:, Od -2:, +…

A: Differentiating the equation and try to eliminate variable to form differentiation equation.

Q: Use undetermined coefficients to find the particular solution to y" + 4y' – 5y = – 1360 sin(3t) %3D…

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

Q: Let y= c1 cos 2x +c2 sin2x be a two-parameter family of solutions of the second-order DE y"+4y=0.…

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Q: (2xy* + siny)dx + (4x²y³ + xcosy)dy = 0 %3D

A: We have to find solutions

Q: What values of α and A make y=A cos αt a solution to y′′+3y=0 such that y′(1)=3

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation

Q: Determine the largest interval in which the unique solution of (t - 3)y +tan ty =t, y(m)3D0 is…

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