Use the variation of parameters to find the general solution of the ODE. y'' - y = ex + 1

Q: find the general solution of the differentialequation and check the result

A: Given: dydx=2x-3

Q: Find the smallest positive root of the function x²|Cos Vx| = 5 using the False-position method. Take…

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Q: a2u Q15// Solve the partial differential equation дудх = tan-lx sin³y ди = y when x = 0 and u = 1…

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Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

A: F(X)= 12x3 +3CSC2X- 5√x - 4π   ∫F(x) dx = ?   Important points: 1. ∫xndx = xn+1n+1 + c2. ∫cosec2x =…

Q: Solve the given differential equation by undetermined coefficients. y'' + y = 6x sin(x)   y(x)=

A: Follow step 2nd .

Q: +xy+(x-9)y=0 2 4 2.

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Q: Solve the differential equation such that the equation passes through the given point (x,y). Use…

A: Given differential equation is: dydx=x-20x Apply variable separable form to the given differential…

Q: Find an approximate value for x (to 2 decimal places) if 5=(3lnx) - (lnx/2) . Find y'' if y =…

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Q: This is on Method of Solution of Higher-Order Linear ODE with Constant Coefficients. Please utilize…

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Q: Solve dy/dx = y -x with y(0) =1 using the linear multi-step method Yi+1 +(3/2)yı -3yı-1 +(1/2)yi-2 =…

A: First solve the given differential equation: Given : y'=y-xy'-y=-x The given differential equation…

Q: Use the separation of variables and represent the pair of ordinary differential equations generated…

A: Given problem is :

Q: Solve differential equetion. = 8X+_5X dx 4-202

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Q: Find a general solution for y'+ (1/x)y = 0, for x > 0. To receive any credit, you must use the…

A: To Find a general solution for y'+ (1/x)y = 0, for x > 0. We use the method of seperation of…

Q: In a mechanical system, the equilibrium equation for designing angle 0 (in radians) is: 5- (2 + V@…

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Q: Use Newton’s method to estimate the solution of the equation x2 +x−1 = 0. Start with x0 = 1 as…

A: Let, f(x)=x2 +x−1  Then find f'(x) using power rule.

Q: Given the differential equation -(승) (중), y" Find two values of r such that y = x' is a solution of…

A: The given differential equation is y''-6xy'-8x2y=0. Let y=xr. This gives  y'=rxr-1     and…

Q: Solve

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Q: n. ²u

A: Given;

Q: Solve the equation after it is complete using the integration factor X : = x + y A differential…

A: We are given the following differential equation.                y'=xx+y We will solve the given…

Q: Use the integrating factor to solve y' = -3a²y + sin(x)e-*, with y(0) = 1.

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Q: An angle Θ is known to vary periodically with time, in such a way that its rate of change is…

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Q: Solve this differential equation. cos⁡x dy+y(sin⁡ x-1 ) dx=0; when x=π,y=-

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Q: Part III - SOLVE the following DIFFERENTIAL EQUATIONS * for partial derivative symbol, use the…

A: The solution are next step

Q: 000 Find the solution of heat equation by Fourier sine/cosine transform, if initial temperature is…

A: Here we use separation of variables. Means we assume that  ......(i)  be a solution of the given…

Q: Find the solution of the differential equation. (sinθ−2rcos^2θ)dr+rcosθ(2rsinθ+1)dθ = 0

A: See the attachment.

Q: solve

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Q: 3. y" + y = sin x

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Q: Solve z2(p2+q2) =x2+y2 by using partial differential equation.

A: z2p2+q2=x2+y2now on re-writing the above equation as z∂z∂x2+z∂z∂y2=x2+y2 ....................1let z…

Q: solve linear and bernoulli differential equation siny(x+siny)dx+2x^2cosydy=0

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Q: Solve x - cos(x) = 0 by Secant method. Use x-1 = 0.5 and xo = 1.0 as the initial estimates. %3D

A: We will find roots till 4 digit repeat

Q: a2u Q15// Solve the partial differential equation tan-1x sin³y дудх ди given that = y when x = 0 and…

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Q: .Find the smallest positive root of the function x2|Cos vx| = 5 using the False-position method.…

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Q: a²u Q15// Solve the partial differential equation дудх tan-1x sin³y ди given that = y when x = 0 and…

A: Given: The partial differential equation is ∂2u∂y∂x=tan-1x sin3y , given that ∂u∂y=y when x=0,u=1…

Q: Solve the given differential equation by undetermined coefficients. y'' + y = 5x sin(x) y(x) =

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Q: Find the general solution for each differential equation. Verify that each solution satisfies the…

A: The given differential equation is, 4x3-2dydx=0 On separating the variables, we get…

Q: —— Solve given differential equation 2(xdy+ydx)+3x2dx=0; when x=1 y=2

A: Here, the given DE is: 2(xdy+ydx)+3x2dx=0⇒2x dy+2ydx+3x2dx=0 Dividing it by 2x dx we have:…

Q: Find the general solution of the ODE.

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Q: Solve given differential equation - ydx-xdy=y3dx+y2xdy; when x=2, y=4

A: The objective of the question is solve the differential equation at particular value.

Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: Use substitution to find a general solution of the differential equation  a)  x^3*y'+x^2*y=y^2…

A: We need to convert Bernoulli equation into linear differential equation form by using substitution

Q: 3 + v 2 3tV di

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Q: Use Newton's method to find solutions of the non-linear equation for five iterations. Show working…

A: Here we will apply the process of Newton's method

Q: Write the first-order differential equation in standard form. (Use yp for y'.) y' = x7y + sin(x)

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Q: Obtain the General Solution. If the differential is homogenous, show the solution for homogeneity.…

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Q: Solve (p2+q2)y=qz by using partial differential equation.

A: Given that, f=p2+q2y-qz=0 ⋯⋯⋯1 The auxiliary equation is, dxfp=dyfq=dzpfp+qfq=-dpfx+pfz=-dqfy+qfz…

Q: A differential equation is considered to be ordinary if it has aone independent variable more than…

A: Option C  One dependent variable

Q: Approximate fls 3 + 2x* using Simpson's rule (n=6), then find the percentage of error after…

A: nhbgk

Q: Determine whether the given differential equations are homogenous or not homogenous. If the equation…

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