8. Find the solution of the equation 1 z =- (p² +q°) + (p– x) (q – y) 2 which passes through the x-axis.

Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: Consider the equation y"-y-2y = 0. Assume that y₁ (1) = ¹ and y₂(1) = e² form a fundamental set of…

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Q: find general solutions (for x>0) of the Euler equation x3y3  -3x2y"+xy'= 0

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Q: Find the general solution to the given Euler equation. Assume x > 0 4x2y" + y = 0

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Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: (c) Using the method of characteristics, or otherwise, find the general solution to Uy +5Ux = 0.

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Q: Q.1 Solve the IVP: y" + 3y' + 2y = 686(t) with conditions: y(0) = 0, y'(0) = -1.

A: The given initial value problem given is y"+3y'+2y=6δ6t       with conditions y0=0, y'0=-1…

Q: Find the solution of the equation 3U,-5U, =0 satisfying the condition U(0, y) = sin y

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Q: Find a continous solution satisfying the equation and the initial condition (1+x²)y/ +2.ry = P(x) r,…

A: we have given a first order differential equation with piecewise function P(x) we need to find a…

Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

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Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: ry - 3ry + y = , 1>0.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: Part III Obtain the particular solutions of the following: c. y°dx + (x* +3xy + 4y* )dy = 0, y(2)=1

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Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: Find the solution of the initial condition problem: j + t°ÿ+ 3t?y = 0, , y(0) = 1, ý(0) = -1. |

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: Q8. Solve the non-homogeneous Cauchy-Euler equation (a) x?y" – 2y = 3x².

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Q: Find the general solution to the equation xy” + 2y'− xy = 0 Using Frobenius.

A: xy''+2y'-xy=0 →l  Let y=∑n=0∞ cn xn+r  ⇒y''=∑n=0∞ cn(n+r)xn+r-1   ⇒y''=∑n=0∞ cn(n+r)(n+r -1)…

Q: Find the complete and singular solutions of the given equation a) z= px+qy+/1+p² +q?

A: Given partial differential equation, z=px+qy+1+p2+q2 To find the complete and singular solution of…

Q: Find the formulation of a particular solution of y"+2y'+ 5y = t² +4t – t²e-t cos 2t without…

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Q: 5. Solve the 2nd- order differentinl equation: d'y dy dr +2 +y=e24 CS Scanned with CamScanner

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Q: 3. Find the general solutions of, (xy + x* )dy + y°dx = 0 b.

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Q: C. Consider the IVP ỷ + 0.25y = 3 + 2 cos 2t , y(0) = 0 2. Determine the value of t for which the…

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Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: Find the general solution of the given Attached equation

A: Differential eq:9d2ydx2+6dydx+y=0The auxiliary eq is 9m2+6m+1=0

Q: 2x Find the general solution of y" – 4y' + 5y sin (2)'

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: find general solutions (for x>0) of the Euler equation x2y"+xy'+ 9y = 0

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Q: 3. Determine the general solution of the following nonhomogeneous linear equations using the method…

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Q: Q5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª. (b) у" — 2у/ + 5у…

A: We are entitled to solve only one question at a time. As the specified one is not mentioned, So we…

Q: Show that the equation Əy 2 a3y + 2k possesses solutions of the form 00 -kt E C,e cos (C, x+ E,) cos…

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Q: Find the approximate solution of the equation Uxx = 4u; by Crank- Nicolson method subject to u(x, 0)…

A: Given: The equation uxx=4ut Initial and boundary conditions: ux,0=0, u0,t=0 and u2,t=2t   To find:…

Q: Find the general equation solution to the 2Zx + Zy +Z = o

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Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: x²y" – 3ry + y = x°, r>0.

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Q: 3. Find the general solution of y" – 3y' + 2y = e" using the method of variation of parameters.

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Q: The solution of the Bemoulli equation y' +2-Vy= 0 is:

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Q: 8) Find the general and particular solution for the following separable equation dy -.5y, y(0) = 2…

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Q: . Find a particular solution to the inhomogeneous equation y" – 9y/ + 8y = e* in the form y(r) = c-…

A: To find A particular solution to the inhomogeneous equation in the form y(x) =Ce^(2x)

Q: 5. = y – xy³e-2x у —

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Q: 2 (a) Find the particular solution of the following equation satisfying the given initial…

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

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Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y?, y(0) = 1.

A: the general form of the Bernoulli equation is dydx+P(x)y=Q(x)yn we have, y'=5.4y-12y2 rearranging it…

Q: Find the general solution to the equation 4(x^2)y''+8xy'+y=0 by the method of Frobenius.

A: The differential equation is 4(x2)y''+8xy'+y=0. Let the solution be y=∑n=0∞anxn+r, then its…

Q: 22.Consider the equation y″ − y′ − 2y = 0. a.Show that y1(t) = e−t and y2(t) = e2t form a…

A: Given the equation y''-y'-2y=0. We need to show that y1(t) = e−t  and  y2(t) = e2t form a…

Q: We wish to find the solution to dy = 26y that passes through the point (x, y) = (1, 3).

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Q: Find a general solution to the Cauchy-Euler equation x°y'"' - 8x²y" + 9xy' – 9y = x², x> 0,

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Q: The solution of y¨ − y = δ (t) −δ (t − 1), with y (0) = y˙ (0) = 0, is given by Select one:

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Q: 1) Find the general solution to the equation y(t) to 2y" + y – y = 3e-t + 2e¬t/2 Using the method of…

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

Q: -B-2-1 -2 -3- -8- 16+ hich equation best represents the linear functi Oy=-5x + % Dy= -5x+ 3 Dy= % x…

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Q: 1: Find the general solution of the following equations: I. dy_2r+2y-3 X-y-1

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.