(c) 6e2z-y (d) x+y ; y(1) = 2 (e) y' +y = e² y(0) = 1 %3D

Q: Utt-4Uxx 0 U(x,0) = x U (x, 0) = x2 Find the general solution of given initial value problem?

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Q: solve the initial value problem. x dy - (y + √y) dx = 0, y(1) = 1

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Q: Find the general Solution of the Partial differential equation (xz + yz)p+ (xz- yz)q = x' + y?

A: This is Lagrang's linear equation so solve using auxiliary equation.

Q: Find the particular solution for initial value problem.

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Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = . √3 2…

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Q: Use Euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the…

A: To use Euler's method with step size 0.1 to estimate y(0.5)

Q: Solve the initial value problem. dy 3 dx - = x˚ (y - 5), y(0) = 9

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Q: Find the particular solution for initial value problem.

A: dydx=8x3-3x2+7x having initial value y3=0

Q: Find the value of X(0.3) for the initial-value problem dx dt = -xt, x(0)=1 using Euler's method with…

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Q: Find the particular solution for the initial value problem.

A: Given, ex dydx-exy=x2-1 ;y(0)=42 dydx-y=x2-1ex

Q: dy =x+3x + e2x dx 1. Solve the initial value problem when x-0. y-2.

A: The given differential equation is solved by variable separable method.

Q: [  (1+ xsiny)dx - x2cosydy = 0  ] How can I find the solution "y" of this equation?

A: We shall use basic knowledge of first order ordinary differential equations to solve this question.…

Q: Solve the initial value problem. dy -=x°(y- 3), y(0) = 8 dx

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Q: Part II Solve the initial value problem. (y°cosr– 3x?y– 2x) dx+ ( 2ysinx – x³ + Iny) dy = y (0) = e…

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Q: Find an explicit solution of the given initial-value problem. x2 dy=y-xy, y(-1) = -4 dx y =

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Q: Find an explicit solution of the given initial-value problem. x20Y = y - xy, y(-1) = -2 dx y =

A: Given initial value problem, x2dydx=y-xy,y-1=-2 Find the explicit solution of this problem.

Q: The differential equation (x+ 2y - 4)dx - (2x + y- 5)dy = 0 represents non-parallel lines.

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Q: What integral equation is equivalent to the initial value problem y′ = ƒ(x), y(x0) = y0?

A: Write y'= dy/dxThen separate the variables.

Q: Solve the initial value problem dy + X, x > 0; y(2) = 0 x3 dx

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Q: initial-value

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Q: Solve the initial value problem. dy = 4 e -X, y(0) = 1, y'(0) = 0 2 dx

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Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. Solve the initial value problem dx - x* (1+ y) = 0, y(0) = 5.

A: Explanation: Given that,  dydx-x6(1+y)=0, y(0) Now,  dydx=x6(1+y)1(1+y)dy=x6dx

Q: y '=x+y2;  y(0)=0 Find the solution of initial value problem with Picard method.

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Q: find the initial value problem dy/dx = e^2, y(0)=2

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Q: Consider the initial value problem dy + x(2y – 1) = 0, for 0 <x < 5, y(0) = 2, y(0) = 1. dx? (a)…

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Q: What is the general solution to the differential equation (x-4y-3)dx-(x-6y-5)dy=0

A: Our Aim is to find the general solution to the differential equation given…

Q: Solve the initial value problem √y dx + (x - 2)dy = 0, y(3) = 9

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Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: The differential equation of the family curve y=c1x³ is Select one: dy а. dx 3x O b. y'=3x O c.…

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Q: Find the particular solution for initial value problem.

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Q: a. Solve the initial value problem dx with y(0) = 4. Use t as the variable of integration in the…

A: I have solved using separation of vsriable method

Q: Solve the initial-value problems. dy _ 1 dy x+1 a.- dx dy - = x²/x³; y(0) = 0 2- y(-1) = 5 ; y(1) =…

A: Solve initial value problems

Q: Solve the initial value problem 2(y- 1)dy = (4x2 + 5x – 1)dx for y(0) = 2 %3D

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: To find the solution of the differential equation we use the method of separation of variables. We…

Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

Q: I know that a higher order differential equation can be turned into a linear system, but is the…

A: Please see the below picture for detailed solution.

Q: 44. The integrating factor of the differential equation x dy + y dx x^2 dx is_. 1 O e^-2x O e^-2y…

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Q: Solve the initial value problem: dy x(1+ y)²; y(0) = –3 dx

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Q: 2x4 +4x3 y″−6(lnx)y‴=−3x3 −2x5 y(4) +7(lnx)y′   What is the order of the differential equation shown…

A: The given differential equation is ,2x4 +4x3 y″−6(lnx)y‴=−3x3 −2x5 y(4) +7(lnx)y′. The order of the…

Q: Solve the initial value problem. √y dx + (x-9)dy = 0, y(10) = 1

A: Sol:- ydx+x-9dy = 0 , y10=1It can be rewritten as :-ydx=-(x-9)dy

Q: cln 4 cln 3 cln 2 10. Compute e0.5x+y-z dz dy dx.

A: Evaluate the integral: ∫0ln4∫0ln 3∫0ln 2e0.5x+y-zdzdydx=∫0ln4∫0ln 3ey+0.5x∫0ln2e-zdzdydx=∫0ln4∫0ln…

Q: function y(t) is a solution of the initial value problem y" + ay' + by = 0,

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Q: . The differential equation (2x³ – xy² – 2y +3 )dx– (x²y+2x }dy = 0 is exact because ƏM ƏN %3D ôx

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Q: Find the solution of the initial value problem dy = -y+e'y?, y(-1) = -1 dt

A: We have to find the solution of the initial value problem…

Q: =e*", y(0)=1. dx Find the solution of the initial value problem

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Q: What are two linearly independentsolutions of the differential equation y''-5y'-6y=0

A: We have to find linearly independent solutions of the given differential equation.

Q: Solve the initial value problem. 3y' – 8y = e, y(0) = a Let ao be the value of a for which the…

A: A first order linear ordinary differential equation of the form  can be solved by using the…

Q: Solve the initial value problem dy/dx=(x+y+1)2-(x+y-1)2  where y(0)=1/2

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