- 2- Solve: (2x +1) a.) dx3 +2y 3e* dx %3D dx2 + 6(2x+ 1)+4y = (2x+1) [t= In(2x+ 1)] %!

Q: Find the general solution of dy d²y 6- dx2 + 12- dx fip - 8y = 21e2 dx3

A: General solution

Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

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Q: a) Find the general solution of the given equations of the line (2x - 5y + 10)dx+ (7x + 3y - 8) = 0

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Q: solve (D^3-3D^2+3D-1)y=x^2(e^x)

A: Solve the differential equation:  D3-3D2+3D-1y=x2exD-13y=x2exy=1D-13x2ex   y=1D-13x2ex  =ex1D+1-13x2…

Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: use elimination method to Solve * - 3x -t 2 2. 1. tP dx 2. tP +3X +8y =2

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Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: 3. Solve for the root(s) of the equation f(x)=3x³-4x²+8x+4

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Q: 3r dθ+4θ dr=r2θ3 dr (SOLVE USING NON-EXACT METHOD OR INTEGRABLE COMBINATION)

A: Given differential equation is, 3rdθ+4θdr=r2θ3dr

Q: (9x-4y+4)dx-(2x-y+1)dy=0

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Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: d²y -6空+9= 0. dx2 dx 业

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Q: Find f by solving the initial-value problem. f'(x) = 7e* – 6x³, ƒ(0) = 5 -

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Q: a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of…

A: As you have posted multiple parts,but they are independent so according to our guidelines we will…

Q: | 2x²+ 4x- 5 x(x² +6x+10)? * To solve | -dx using the method of partial fractions, we write it as

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Q: Solve the equations by the method of undeterminedcoefficients

A: First, consider the homogeneous case d2ydx2+7dydx=0. We solve the auxiliary equation as…

Q: Solve second order DE y" - 4y' + 4 = 0

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Q: x+y-4) dx-(3x-y-4)dy=0; when x=4, y=1 Solve using Coefficient linear in the two variables

A: ( x+y -4)dx-(3x-y-4) dy = 0 , x=4                                                               y…

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

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Q: 3. Find the general solutions of, x+y dx x-y, a.

A: We have to solve the given differential equation.

Q: d²y dy Solve 4 +4y = 3e2x. - dx2

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Q: Evaluate the intergrals. ∫ (x-1) dx / x2+5x+6 show the complete solution. step by step

A: Given integral is ; ∫x-1x2+5x+6dx

Q: Find the general solution using the method of undetermined coefficients. dx +7x=8e° dt -41

A: Answer

Q: Solve for t. 4 - 1 - 1 =D4 - 3 -3

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Q: Solve d2y/dx2+y=cosecx by using method of variation of parameters.

A: Consider the given differential equation d2ydx2+y=cosecx

Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

Q: What is the general solution of ху(ху5 - 1) dx + х?(1+ ху)dy3D0 ? A 2x3y5-3x² = cy? B 2x°y3 - 3x2 =…

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Q: Find the particular solution determined by the initial condition. f'(x) = rx) = 2x2/5 - 3x, f(1) =…

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Q: -solve the following system by using the method of undetermined coefficients. dx1/dt= 2x1-5x2-cost…

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Q: 4. The Quadratic equation whose roots are 1 and %. c. 2x-3x+1-0 a. 2x +x- 1- 0 b. 2x-3x -1 0 d. 2x…

A: Hello, thanks for the question. We’ll answer the first question since the exact one wasn’t…

Q: Find the family of solutions of the equation (x2y5 + y3)dx + (x3y4 + x)dy = 0

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: (24) Solve : (n²y = 2xy²) dn. - (n²³-3n² y) dy zo

A: Solution

Q: Solve the dff oq dy 3x寸票-5-2 %3D

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Q: d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above…

A: Here is the, solution

Q: Q2/ By using partial method solve fx² In x dx

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Q: Solve (D2+4D+4)y=e-x sin 2x

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Q: Solve the equation xd2y/dx2-dy/dx+4x^3y=x^5

A: Consider the provided D.E,

Q: Use variation of parameters to solve y'' - 7y' +10y= e^2x.

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Q: An initial population, p, of 1000 bacteria grows in number according to the equation 4t p(t) =…

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Q: 5. (y-2)dx-(x-y-1)dy 0

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

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Q: (y2-2xy-x2)dx+(2x2)dy        Find the solution of the equation through the point (1,2)

A: We have to find the general solution from the given condition

Q: Solve:- dy 3y -4 x" こ メlo

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Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…

Q: Find the particular solution of (d2y/dx2) = 4x3 - 2x; y' = 4/5 and y = 1 when x = 1

A: Given differential equation, d2ydx2=4x3-2x       ...(1) y'=45 and y=1 when x=1