Q2 :Given that the equation x² – kx + 8 = 0 where k ER has one of the solutions is %3D x = 2 - j2. find the second solution and the value of k

Q: Use the graphical method to solve the equation.

A: Given, 2x+1+1=x

Q: Q4: Solve the following DE by the method of variation of parameters: y" + 2y' + y = e-*Inx

A:

Q: 2. Use the method of undetermined coefficients to solve the equation y" – 3y + 2y = e +2.

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Q: Solve x?y" – 2ry' + 2y = x³ In x by first finding the complementary solution and then using the…

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Q: 7. Find the solution of the DE: (D? + 9)y = x+e2 using method of undetermined coefficients.

A:

Q: Use Variation of Parameters to solve the DE y′′ − 4y = e^(2x)/x

A: Y" -4y =0 D2 -4 =0 D =2,-2 Y = c1e2x + c2e-2x Now find  W = (e2xe-2x2e2x-2e-2x|…

Q: Q12: What is the formula of The general solution for a D.E. with variable coefficients about…

A: Given x0 is an ordinary point of the differential equation.

Q: Q4: Find the general solution of 1-st order Linear D.E (x2 + 9) 2 + xy = 0

A:

Q: Q4: Solve the initial value problem: ty = 2y +t %3D

A: The general solution is, y = y(t) = t³ + t²•C, where, C is the constant of integration.   The…

Q: Q2. If the solution of the below first order D.E is y = C ef(x,y) (x³ + xy²)y' = y3 Find the f(x,y).

A: x3+xy2y' = y3dydx=y3x3+xy2 ........................equation(1)Let put y = vx in equation(1) and…

Q: Find general solution of " – y – 2y = e2t

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Q: Q4: Solve by using Separation of variables method? ди =k - for 0 0 at ´əx² u(0,t) = u(L,t) = 0 for…

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

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Q: Q2. If the solution of the below first order D.E is y = C ef(x.y) (x³ + xy²)y' = y3 Find the f(x,…

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Q: ) Use the method of Undetermined Coefficients to find the general solution to the DE y" – 3y + 2y =…

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Q: Find the General Solution: y" - 3y' + 2y =e*

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Q: (4D* – 4D³ – 23D² +12D+ 36)y = 0

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Q: Using the variation of parameters, find the particular solution of (D2 +1)y = secx

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Q: When solving S3x – 2y = 5 ly = 3x – 3 by the substitution method, we obtain x = , so the solution…

A: Given equations are: 3x-2y=5......(1)y=3x-3......(2) Get the value of 3x from the equation (1)…

Q: Using the method of undetermined coefficients, write the form of the assumed particular solution for…

A: Given: y"+2y'+y=x2e-x Auxiliary equation are,  m2+2m+1=0 (m+1)2=0 m=-1,-1

Q: Q2. If the solution of the below first order D.E is y = C ef9) (+xy)y=y Find the f(x, y).

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Q: у" - у' + 4y %3D 0; у(-2) %3D 1, у'(-2) %3 3

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Q: Using the method of Variation of Parameters, the form of the particular solution Y, for the NHLDE 1…

A: Use the procedure of method of variation of parameters to solve this problem as in next step.

Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: Q4: Solve by using Separation of variables method? = 4 for 0 0 (0.e)=27.t) = 0 for t 20, u(x.0) =…

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Q: Q3/ find the general solution of the following PDE yzx – xz, + x2 –- y? = 0

A: The given PDE can be written as  yzx-xzy=y2-x2

Q: Q4: Solve the initial value problem: ty' = 2y + t³

A:

Q: Q2/ solve the D.E. by variation of parameters Q2/ solve the D.E. by variation of parameters d?x dx +…

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Q: y"+ 4y = x What is the particular solution y.? Yp

A: helar we have to find particular solution of the given differential equation. the solution is…

Q: solve the given initial value problem. Describe the behavior of the solution as t → ∞.…

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Q: Find the general solution to: 3X y^ - Gy' +Qy= x*e*

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Q: у" - 4у 3D -7е2х + х; у(0) %3D 1, у((0) — 3

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Q: ~2V3 2/3 43 dx V16 – x² -

A:

Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x' + xy?)y' = y³ Find the f(x,…

A: Given that The solution of th given D.E. is  y=Ce^f(x,y)

Q: (i+z) dy 3. Solve (itx) 9

A:

Q: Solve the 2nd order D.E. below using method of undetermined coefficients : y''+ 7 y' = 42 x^2 + 5x…

A: To find the solution, first, solve the homogenous ODE, y''+7y'=0 and obtain yh=C1+C2e-7x.…

Q: Using the method of Variation of Parameters, the form of the particular solution y, for the NHLDE 1…

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Q: Given (E1): y(x – 5)dx – x²dy = 0, with y(1) = 1. The solution of the following IVP (E1), by…

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Q: Qi) Solve the following PDES by direct integration. 2) = 0 дх ду 3) = x?y %3D дх ду dxdy azu -2t and…

A: Solve PDE by direct integration.  According to guidelines we solve only first question.

Q: Specifically a differential equations problem. Question in pic below.

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Q: Find the value of k so that the value of (2y - 1) dy is 10.

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Q: 4. Find the constant a so that Ø(x) = xe2x is a solution to y' + ay – e2x = 0 А. 4 В. 1 C. -1 D. -2

A: We have to find a

Q: a²(xdy-ydx) x²+y2 5. Solve xdx + ydy = using exact D.E method.

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Q: 3. 2y" + у' %3 А. 3 В. Зx2 С. Зх D. x?

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Q: Solve for x given a). e2-3x = 5 b). In(5x – 1) = –-1 c). e2x – 5e* + 6 = 0

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Q: ds Find the solution 2- dt S 5t3S3

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Q: Use the Gauss-Seidel method to solve the following system until the percent relative error falls…

A: The gauss-Seidel method uses the iterations to solve the system of linear equations. The iteration…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.