y"- 5y + 4y ez.

Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation,…

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

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

Q: Find the solution. 2y" - 3y' + y = 0 (A By = c,e 1- ©y = c,e Dy =c,e

A: Find roots of  characteristic  equation  of given differential equation .If roots are real and…

Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: Solve the DE y'=(x+y+2)^2, y(0)=2 by setting u=x+y+2.

A:

Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: S Sz(x² + y³)dxdy, wherein B = {(x, y) E R²; 0 < x² + y² <4}.

A: Double integral

Q: Find the solution for the given DE. y +4y e", y (0) = 2 %3D y = -te" + 2e y = te+re y = te" + 2ee y…

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Q: (c) S, y*/1- y² dy

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Q: Let y(x) be the solution for the DE : y = (x + y – 1)2 If y(0) = 1, thenfind y(4)

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Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

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Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: What could be the potential equation ? y² = 2? + x? a. 4y = z2 +x? C. z? = y? + x² %3D d. x² = y2 +…

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Q: (a) x²y "-xy '+ y = Inx %3D

A: According to our guideline, We can solve only first question of multiple question.So here we solve…

Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: y' + xe*-y = 0

A: The solution is given as

Q: Solve the IVP y′′ + 2y′ + 5y = 8e^(−t), y(0) = 0, y′(0) = 8

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Q: f(z, 9) = 82" + 5y² + 4z°y+ e7=y of Calculate

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Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: 2. JO (y+5) dy (y-3)

A:

Q: Solve the IVP y" – y + 0.25y = 0 with y(0) = 2, y' (0) = 1/3 y(t) = 2e/2 – ?et/2 - O _ 꼭et/2 y(t) =…

A: Given y"-y'+0.25y=0 with y(0)=2 , y'(0)=13

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: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a have a…

A: Given: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a…

Q: 2,t-3P dt, then %3D 12

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Q: Dyy 2y-x; %3D

A:

Q: • Jeze 39. et dt e²t + 3e¹ + 2

A: Given integral is I=∫etdte2t+3et+2 To evaluate the integral.

Q: in yy = 2 y-x; %3D

A:

Q: dy 4. x2 + y? = dr xy (Bernoulli DE) %3D

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: Solve the equation ru, + (x + y)uy = 1 %3D on dof:

A: In this question, we solve the partial differential equation by using characteristic method.

Q: Obtain the general solution of the following: A. (D2 − 1)y = ex + 1 B. (D2 + 1)y = sec3x

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Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: (D² – 3D + 2)y = e2*(1+e2x)

A:

Q: (2, 3), dy If x2 + xy = # = 10, then at the point dx

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Q: Find the General Solution dy dr = y? – 3y²cos (x) 1.

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

Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: dy + ydx %3D = 3x²y?dx,

A:

Q: Obtain the general solution unless otherwise instructed a.) (9D4 + 6D3 + D2)y = 0 b.) (4D4 − 45D2…

A: (a) Consider the given equation. 9D4+6D3+D2y=0 Convert the equation into the characteristic equation…

Q: a) Let y" + xy' + y = 0 be given. Why does the approach y(x) := e^× does not work?

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Q: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Find the general Solution of DES 2x y Y' = x? +2y} %3D

A: SOLUTION-

Q: Find the general solution of (x³ + 2y4)y' = 3yx² in implicit form f(x, y) = c. When y(0) = 1, what…

A: We have to solve the differential equation

Q: Show that y = c1ex + c2e-x + c e + 3 is a solution of y ||| -2y | | - and | + 2y = 6 (justify).

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Q: For what values of m does Y = emx satisfy Y" + Y' - 2Y= 0 ?

A: For what value of m does Y=emx satisfy Y''+Y'-2Y=0

Q: 'ind the general solution of d³y 6. dr3 dy - 8y = 21e2 dr dr2

A: