Solve the differendialegimaition: (2x+e)dx + (xay co

Q: (c) | Vtan(x) sec (x)dx 3

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Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: solve homogeneous equation by linear method 2. x(dy/dx) + y = x*sinx

A: We use linear differential equation method

Q: Find the root of e^-x ( x^2 + 5x +2) +1 = 0, using the secant method with initial guess -2 and -1 to…

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Q: SOLVE USING INTEGRATING FACTOR 3y 3x²y +2 ) dx + (2x* +6 In x) dy = 0 3.

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Q: By Simpson's method, find an approximation for [(x³−2x³)dx_(n=4) 0

A: What is Simpson's Rule: Simpson's rule is a tool to approximate an integral. It is the process to…

Q: the metrod of variation of parameters to Apply Solve my = Secnn dx2

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Q: Find the general solution of

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Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Use Milne's method to obtain the value of y(0-3).

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Q: Find the general solution of y'= sin²xcosy.

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Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: • Use the trapezoidal rule with n = 14 to estimate: -dx √√1+x²

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: The general antiderivative determined by - x² - 3x +2 is dx

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Q: 4. Using homogenous D.E approach, solve (x³ – 3xy?)dx = (y3 – 3x²y)dy.

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Q: c) Use trigonometric substitution to integrate dx 4-x2

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Q: S csc“(3y)dy

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Q: Y2-1 dy

A: Follow the procedure given below.

Q: Solve by the method of successive approximat ion

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Q: Find the general solution: k^2 dx+(x-y+k)^2 dy3D0

A: Given that: k2dx+(x-y+k)2dy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: Integrate by Gaussian quadrature (n=3). dx Ji 1+x*

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Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: . Approximate the value of V65 by Newton-Raphson method letting xo = 5.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: . Solve the first order equation (3z²y + 2ry)dx + (x³ + x² + 2y)dy = 0.

A: Solution

Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

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Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

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

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Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

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Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: What integrating factor should be used to find the solution of the equation ydx + (xy + x- 3y) dy =…

A: Given that: ydx+(xy+x-3y)dy=0

Q: Find a root of an equation f(x) = x^4-2 using Halley's method.

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Q: Find oy for dx2

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Q: Obtain the general solution of x^2 d2y/dx2 -2xdy/dx+2y=sin(lnx)

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Q: D ifferentiate. a. y = sin(2x3 – 3) 5-3Vx+x5 b. y = x2

A: Please refer to the image below.

Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: Integrate both sides = S sec²y dy = S dx

A: ∫sec2y dy=∫dx

Q: 1 B3. Evaluate dx, using substitution method.

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Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: dx 4√/3x-x² 5³-

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Q: (b) Integrate x-³e-l/a², dx

A: Here we can find the answer as below.

Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: dx 4. S x²Vx2-9

A: 4). Given: I=∫dxx2x2-9   ....(1)   As we know from the trigonometric identities; 1). cosx=1secx 2).…