(D++D²)y=3x²+4sin(x) – 2cos(x) 2. MUC:

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx -…

Q: 3. Solve the particular solution (D² + 3D + 5)y = 5e¬*sin2x using D- operator method.

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Q: Obtain the particular solutions of the following: (y-Vr² + y² \dx– xdy =0, y(0)=1 a.

A: Solution is given below:

Q: C3x -y sin xy) de - x sin sy dy o HSin

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Q: try also solve this by Variation of Parameters method! Solve the following initial value problem: y"…

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Q: Exercise: Use reduction order to find a second solution y2(x) 1. y" + 16y = 0, yı = COs 4x

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Q: F(x) = S 43x dx u = 3x; du = 3dx 3 F(x) = S 43x dx 3 1 1 C43ra

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Q: carctan3/2 3 sec x y dy dx

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Q: Find the particular solution of y' = xey-x? given y(0) = 0.

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Q: Find a general solution of the equation: 5xy' = 2 – y %3D

A: Please find attachment for the details solution

Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: How can we solve this separable equation? N(y) * dy/dx = M(x)

A: The given differential equation is, Where, N(y) and M(x) are the functions of the variable y alone…

Q: Solve this DE in Non-Exact method: (x2+6y2)dx-4xydy=0 ; y(1)=1

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Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

A: Given query is to find indicated derivative.

Q: Use the method of undetermined coefficients to find the solution to y''+y=4x+10sin(x) that is…

A: Method of undetermined co-efficient: For given a non- homogeneous ODE of the form…

Q: Obtain the general solution: 1. (D² + 25)y = -50 sin 5x

A: First we will find the complementary solution corresponding to the homogeneous part of the…

Q: Find the General solution Use method of undetermined coefficients. 1. (D² l)y=ex (2sinx + 4cosx).…

A: To Find: the general solution using the method of undetermined coefficients   1. D2-1y=e-x2 sin(x)+4…

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

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Q: Obtain the general solution unless otherwise instructed d²y 1. dx2 - y = 10sin²x

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y?)dx + xy dy = 0

A: We will solve the problem

Q: 5. Given that a cubic equation x° + ax² + bx +c= 0 has zeros a, ß and y. Show that aßy = -c.

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Q: (S+2) (s?+u] solve by using partial straction

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Q: Find the general solution of a given non exact DE y(8x-9y)dx+2x(x-3y)dy=D0. (Note: Express your…

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Q: 2 Y Sin y - yy 3=c C- %3D

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Q: Determine the form of a particular solution y, (x) for y" - 4y'+5y e*+xsin 3x- cos 3x. [Do not…

A: Solution: The given differential equation is y''-4y'+5y=e5x+x sin3x-cos3x. For the complimentary…

Q: 2. Obtain the particular solution when x = 1 and y = 1 y(? - y? + 1) dx – x(x² - y? - 1) dy = xlx? -…

A: Here is the solution of the given differential equation.

Q: Q/ Solve the DEs: 1-a+ykdx+(1+x*)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

Q: solution of the di dy x + 4y = * x2

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Q: Test the DE for exactness then solve. 5. (3x2 + e2y)dx + (2x e2y – 4y)dy = 0

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Q: Obtain the general solution unless otherwise instructed 1. arž -y = 10sin²x dx² SUMMARY OF ANSWERS…

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Q: Solve the @iven dif frerenticul equation uning the variables method of seperatio n of dy 4y+3

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Q: 5. e²y$/1- e' dy

A: Solve the integration

Q: y sin x - xy² = c C

A: We have to form the differential equation by eliminating the arbitrary constant.  Here the equation…

Q: Using the method of variation of parameters, the form of a particular solution Yp of (D²+25)y=4x²…

A: First we need to check complementary solution  So, consider homogeneous equation÷ D2+25=0 Auxiliary…

Q: Obtain the general solution: 1. (D² +25)y = -50 sin 5x

A: Using method of linear differential equations with constant coefficient.

Q: Q1) solve all these first order diff questions with appropriate method of solutions dy _ y²+xy?…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: | 2² (x³ + 5)°dz. Use substitution to find the antiderivative of [Show Solution] Hint Multiply the…

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Q: SOLVE THE NHLDECC USING UNDETERMINED COEFFICIENT. (D³ + 4D² + 9D + 10)y = -24e-* when x = 0,y = 0,…

A: Topic:- solutions of differential equations

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

A: Here is the, solution

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

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Q: (D++D²)y=3x²+4sin(x) – 2cos(x)

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Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: Obtain the general solution to the equation. * + 2x = 4y° dy The general solution is x(y) = |…

A: To obtain the general solution of the Linear Differential Equation

Q: H.w Solve y'+y'-zy= -2 f yoj=Zfylcojal

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Q: (Think homogeneous) Solve explicitly (y² - xy) dx + x²2dy = 0

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Q: test for the exactness and solve the IVP, critically outlinethe particular solution. (x + 5exy)dx…

A: Given differential equation is x+5exydx-exdy=0, y0=-2

Q: 2 = 3x° (7 + y²) dx

A: Here equation is separable so w separate them and apply integration.

Q: Solve the bernoulli's equation x(6x^2−y−1)dy +2ydx =0.

A: The given Bernoulli’s equation can be written as:

Q: (15pts) Identify (write down) the type of DE, and find the general solution. (y- 3x)dy = (x +3y)dx…

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