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

Q: classify and find genoral solution of differe equaton :- (l-2x² tany) dx– (x³sec^y ) dy=o

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Q: Find dz/ax andðz/@yif I z = x* sin(xy³).

A: If a function f(x, y) is to be partially differentiated with respect to x, then we treat the…

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: Find the solution of the IVP: y" – 9y = sin 2t, y(0) = 0, y'(0) = 1 using method of undetermined…

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Q: Solve the IVP y"(1) +y'(t)- 2y(1)= 2e' sin(t), y(0) = 1, y'(0) = 1. %3D

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Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

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Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

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Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A & b are arbitrary constant.

Q: b) Solve by using Runge-Kutta method to find y,. dy = x + cos(y) ; 0Sx<1 ;y(0) = 1; h = 0.5 dx

A: Solve the intial value problem, using Rung-Kutta method

Q: x°y" + 2x?y"+ xy'-y=0

A: A homogenous linear differential equation with variable coefficients given by,…

Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: The longest interval in which the 1.V.P y" +(tanx)y- xy = x, y(1) = 3, y'(1) =0 surlay has a…

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Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

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Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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Q: What is the functional form of the particular solution V + y = sin(2t) + sin t

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Q: B. Solve the DE. x²y"+ xy' + y = tan (Inx)

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Q: dx + AIX y = cos x, y(n) = 0

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: Find the general solution of (y + 2y) sin r²dr + V1 dy = dp. 0. %3D

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Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

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Q: Solve the DE Coshx dy+(ysinhyte) de =c 3D0

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Q: Use undetermined coefficients to find the particular solution to y"+ 5y' + 4y = - 500 sin(3t) Y(t) =

A: We have to find the particular solution of  y''+5y'+4y=-500sin(3t) by using the method of…

Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

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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: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

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Q: .2 x cos?y dx + tan y dy = 0

A: The given differential equation is  x cos2y dx+tan y dy=0 Solving the the given differential…

Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Find the general solution of y" – 4y' + 5y = sin (x)

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: Eliminate the arbritrary constant/s. Show full solution. x= -In t, y= at + bt?

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Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

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Q: Find the particular solution of dy - 2y = x³ sin 4x, y(1) = 2. dx %3D -

A: Using method of Linear Differential Equation.

Q: The longest interval in which the 1.V.P y"+(tanx)y- xy = x, y(1) = 3, y'(1) = 0 surlay has a…

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Q: 1) y= y(x) is given implicitly by 1+xarcsin y – 2y cos.x = 2xarctan(-). Find y' at y point 0). the

A: First we will differentiate the given equation with respect to X. Plugin x is equal to pi by 3 and y…

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: h of the DE's =)y = 2 sin² x ; y(0) = 0 , y'(0) =-2

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Q: 25) y" + y = 2 cos(t), y(0) = 2, y'(0) = 0.

A: Use second order differential equation

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

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

Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

A: Partial derivative of a function of two or more variables with respect to one variable is the…

Q: y"+y = e" what is the nonhomogenous(particular) solution of the given differantial equation?

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Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Verify that y = x[cos (Inx)] is a solution of x²y" – xy' + 2y = 0

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Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution is given below

Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)

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.