1 of 1 Assignment 1. Solve the initial-value problem y' - 2y = e, y(0) = 3 2. Solve the initial-value problem y" + y = e 21 sin t, y(0) = 0, y'(0) = 0. 3. Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) = 0, y'(0) = 0, y"(0) = 3.

Q: Q1) solve the following differential equation 2- 3- y² (cos x +)dx + (e² + 2yIn(x))dy = 0 (sin³ (x)…

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Q: 4x(1-x)y"+y'+8y=0 Solve Gauss' hypergeometric differential equation

A: Let Its general solution is given by where,

Q: solve the equation 2xy" +xy'-y 0 5. 2 1 Does y() = x- real s y(1) =1, y'(1)= 2 solve the IVP

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Q: Form the differential equation by eliminating the constant 'a' from r=2a (sin 0- cos 0)

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Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: Solve by UC method  y'''− 6y'' + 11y′ − 6y = 2xe^-x I just need answer for this part

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Q: xy (yе" сos 2 x - 2e% sin 2 x+2x +(хе" сos 2x - 3) у'3D0

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Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: y' + }xy = sin(x 4e¤2 y3 1

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Q: Find a particular solution yp for the equation. y" - 6y' + 5y = cos3x 3sin3x

A: Consider a non-homogeneous differential equation of the form a(x)y''+b(x)y'+c(x)y=r(x). Then the…

Q: Q.3 Solve the differential equations by all possible methods (mention name als (1) 2xye("/>) dx –…

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Q: 1) Solve the differential equation (2° + y° Vz² + y² ) da - + y² ) dy = 0.

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Q: 13) Solve the third-order differential equation y"" + 4y': = sec 2x by variation of parameters.

A: The  given equation is  Comparing the given equation(2)  with  the  We have ,The auxiliary equation…

Q: 2) Solve the following differential equation 6y dx-x(2x'+y)dy =0

A: first we identify the given first order differential equation and find if it can be converted to…

Q: Find the solution of the equation M a²z a²z = e cos y Əх² ду? which tends to zero as x→∞ and has the…

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Q: Different Equation 1. (cos(x) — 2xy) + (e^y -x²)y' = 0; y(1) = 4 2. y' = 3x² -2; y(1) = 5

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Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: Consider the differential equation for y (- 5ӕ — у)da + xdy — 0. ON 1. Express the equation into the…

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Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: Solve y" - y' = xe characteristic equation using undetermined coefficient. Show all your work. The 2…

A: To solve the differential equation y''-y'=xex using undetermined coefficients.

Q: y"+y=82 (t) cos(t), y(0) = 0, y'(0) = 0

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Q: Solve the following nonhomogenous differential equation: d''''y/dx'''' + 2(d'''y/dx''') +…

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Q: 1. Solve y' + 3x²y = cos(z)e with y(0) = -3.

A: Sol:- y' +3x2y=cosxe-x3A first order linear ODE has the form of y'x+pxy=qxy'x+px·y=qxpx=3x2,…

Q: 1. y'=y-xy³e-²x

A: According to guidelines i solve first question only. So kindly request you to repost the remaining…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.