09 10 11 Problem: Find the solution of the following equation. 2 Judu + 2 du_y² ду au и u (X₂6) = 2x

Q: 3.2 Solve the following DE: (y + 4x) y' = 2y - x

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Q: If y=u³ and u=2x³ +2, find when x = 1. dy dx dy dx x=1 (Simplify your answer.)

A: The objective of the question is evaluate the derivative at x=1.

Q: Solve the following: a. If z = sin(5x + 3y) Find and dx dz ду b. If z=(3x+2y) (4x-5y) Find Oz dz and…

A: a. Given z=sin(5x+3y), find ∂x∂z​ and ∂y∂z​. Solution: z=sin(5x+3y) 1. Find ∂x∂z​:…

Q: Find the general solution of the following equations (The answer can be given either explicitly or…

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Q: find the correct form of yp. Do NOT solve for the Don't forget to state y. and yp. coefficients Yp…

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Q: solve using the appropriate method.

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Q: Consider the following equation. 12t - 6t2 -dt =D0 t One solution to the equation is x = 3. The…

A: ∫x312t-6t2tdt = 0one solution is x=3other solution, x= ?

Q: Solve the following exact equation. 4xy² + 2y + (4x²y + 2x)y' = 0

A: Exact differential equation: 4xy2+2y+4x2y+2xy'=0. To Find: Solve the above differential equation.

Q: 1. 1 a) Solve y" - 5y" +19y'+ 25y = 0

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Q: Find general solution, y., and particular solution y, of the following: (only solve for coefficient…

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Q: solve d' - coS 37 dx

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Q: 3. Solve (2 + 3x)² + 3(2 + 3x) -36y= ax² + bx + 1 + 2 sin ln(2 + 3x). dx²

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Q: Solve for the general solution (4ху +3у — х) dx +x (x+2у) dy %3D 0

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Q: find y' if y 43 -2 = 2 2m² +5c8cm) (3 cotm-m² 3Гm + cosm

A: We use  Power rule ddxxn=nxn-1 ddxcscx=-cscxcotxddxcotx=-csc2x

Q: Find a particular real solution for each of the following equations. The reasoning behind your…

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Q: 4. Solve dy d.x. 3y² - x² XU . Note: your solution may be left in implicit form.

A: Use variable separation method after y substitution to solve.

Q: 6. Solve the D.E. 2y" + 18y = tan(3x). %3D

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Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: In which form should one look for the particular solution of y" − 2y + 2y = x²eª cos(x) (you do not…

A: Given DE is  y"-2y'+2y=x2excos(x) ......(1) We find form of particular solution of DE (1).

Q: 2.(a) Using the method of variation of parameters, find a particular solution of the nonhomogeneous…

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Q: 24. Solve 6sin³ x - - 13sin² x + 2sin x + 5 = 0. x € [0,27]. Determine exact values, if possible,…

A: Given equation is 6 sin3(x)-13 sin2(x)+2 sin(x)+5=0 for x∈[0,2π]   To Determine exact value, if…

Q: Using Undertermined Coefficients, solve the following: 4. 4y" +4y' + y = 3xe*

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Q: 3. Solve as a Bernoulli's equation 2 dy dx xy 3 = x + y

A: Solution:

Q: Solve the equation y' = Y 4x²y + x

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Q: 1 0 5) Solve the equation x'=| 2 1 -2 ). x X 13 2 1

A: The given problem is to find the solution for the given matrix differential equation.

Q: 3. y" - 2y' = ex (x² + 2) cos2x 4. y" - 2y' - 3y = 4x - 5+ 3xe ²x

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Q: 2. Solve the diophantine equation x = y'.

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Q: 1. (a) Find ? ; (u²quv). ди

A: To find the partial derivative with respect to u

Q: 10-4z .5-2x-y 6z2 dz dy dx

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Q: 2. Solve the following Bernoulli equation: xy' = y - xexy²

A: Given differential equation is    This can be written as      Substitute, , then we get   Thus,…

Q: 1. Find using Method of Undetermined Coefficient (MUC): y(3) + y(2) + y(a) + y = 2e-2* – 4x° + cos…

A: 1. Given : differential equation         y3+y2+y1+y=2e-2x-4x2+cos3x, y0=-3, y'0=-1, y''0=2…

Q: Solve the following equation using variation of parameters. 1 y" + 3y' + 2y = 1 + ex

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