The Particular Integral for the Euler Cauchy Differential Equation d²y dx2 dy -3x +4y =x5 is given by dx | O a. x³ Inx O b. x Oc. x5 4 O d. X(Inx) 6.

Q: r² (x²– 1)(x² + 1) , What is the resulting value of the definite integral dx? х-1 O 33 1 + 4 15 O 31…

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (4,1,1)…

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Q: 3. (1+2x − ¹) dx (assume x > 0)

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Q: y X-1 dr f In (2x-2) + I dy y. = 0

A: Given DE [yx-1]dx + [  ln(2x-2) + 1y]dy = 0standard form of equation Mdx + Ndy = 0

Q: '0 8 3 تر محمد (1 + x)5 dx

A: According to guideline we need to solve one question. Rest of the questions should be reposted.

Q: メy+(x+1)y= 3xte 2. メ

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Q: Using the substitution u = x³ – 1, ƒ±₁ x² (x³ — 1)5 dx is equal to which of the following? O O 63 -2…

A: Let, Put

Q: Find the following indefinite integrals. (» /= +1 dx. (a) x2 (b) / : re dx. xe' 2.x +1 dx. x2 +1 (c)

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Q: Solve the following differential equation use integration method d²x 1) dy2 2x +2y-= 0 2) - dx 2x3

A: Given differential equations are 1)   y''+2y-2x/y=0    (second order Non-linear D.E) 2) y'''=y/2x^3

Q: d'y dx dy Solve x x- dx +4y cos(log x) +x sin(log x)

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Q: 23x+3+42x-1 6. S dx 2x+3 In(sin x) 7. S- tan x | Voty csc' y dy 8. dx 9. x log 10 x e" dr 1 + e" 10.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2-if y³ = ln xx

A: Please refer to the image below

Q: a. Set up an integral for solving y(x) = + y(x) = dy dx t = t = = x² + x when y(4) = 10. b. Evaluate…

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Q: Compute 0 O-1.5 O-1 1.5 01 L₂ f(x -2 f(x) dx.

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Q: 53. df = (x+ 1)ye"dx + xe*dy

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Q: 3. (1 – 3 sinh( 2t) + sinh(4t))´ dt

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Q: Show that the following equation has a unique strong solution { dX₂ = ln(1 + X²)dt + XedB₁, Xo = r,…

A: To understand the solution I mentioned theorem 1 and 2 for your understanding.

Q: Rocky Mountain Chocolate Factory (RMCF) founder and president Frank Crail employs 220 people in 361…

A: for net price  equivalent rate determine first find the complement of the chain discount rate…

Q: Evaluate sin (4x) dx

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Q: luate 2 Af ² (x-1) 25 dx 7 S² √4+3x dx 1 x² (1+22³)5 dx esinx cosxdx O 플 the definite O inte

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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.