Let y (t) be the solution of the initial value problem y" – 4y' + 5y = e-2t %3D 1 and y' (0) = 17 y (0) 17

Q: 2 What is the solution of the initial – value problem d²y =X O with y(0) = 1 dx? and y'(0) = -2 ? у…

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Q: y" + y = 0, y( »(;) = = 10, y'(x/3) = - 20

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Q: Find the solution to  x' = y - x + t y' = y if x(0) = 2 and y(0) = 4 x(t) = ? y(t) = ?

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Q: Find the particular solution of y' =(2x)/1+2y y(2)=0

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Q: Solve the initial value problem. y(x) = = x³y" + 7x²y" - 2xy' - 10y = 0 y(1) 1.3, y'(1) = -10.1,…

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Q: Solve the IVP 2y"+5y'-3y=0 y(0)=-5 y'(0)=29 y(x)=?

A: The given differential equation is                                                   2y''+5y'-3y=0…

Q: Find the solution to x' = y y' = 12x + 1y if x(0) = 0 and y(0) = 8

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Q: y" – 2y' + y = x², y(0) = 3, y'(0) = 2. -

A: y′′ −2y′ +y=x2 Second order linear non−homogeneous differential equation with constant…

Q: Find the solution of the initial-value problem dy - 2y = 2.x", y(2) = 8. dx

A: Convert this IVP into linear differential equation by dividing by x then proceed to fund Integrating…

Q: 1 2x {y =—=—e² + 1. 2y'+3y=e²x {y= 7 + се 3x/2

A: We have to solve the differential equation2y' + 3y = e2x

Q: Solve y'' + 9y = 8(t – 2), y(0) = y'(0) = 0 y(t) = for t 2

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Q: (b) Solve N +e*f + (1+x*)y = 0, %3D near x = 0, if y(0) = 1; y/(0) = 0. %3D

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Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

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Q: y' = 2t(1 + y), y(0) = 0 Investigate the existence and uniqueness of the initial problem.

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Q: 3. Find the solution of the initial value problem xy" + y' = x²(y/)², y(1) = 0, y'(1) = 1. What is…

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Q: y" – 2y' + 2y = 0, y(0) = -2, y'(0) = 1 %3D

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Q: Find the solution to x'=y y'=4x+3y if x(0)=0 and y(0)=2 x(t)=? y(t)=?

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Q: y'

A: The function is given as : y'''-y''-2y'=0. To find the general solution of the function , The…

Q: Use substitution method

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Q: Solve the initial value problem. (x² + y² -5)dx =(y+xy)dy: y(0)=1 b.

A: To solve the below initial value problem. x2+y2−5dx=y+xydy,  y0=1

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: ==== 3y' - y + 6ety3/2 = 0, y(0) = 1/4.

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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.