(3) Solue the Initial Value Probles -that SatieSFies the Compleme equation (+) yM -2(x+ Dy! 13 ! %3D gl0)31,4(o) = 1 and Y2 gro) =1 and Yn %3D

Q: 4 ( Calculate -2x dy

A:

Q: Solve 4y'' + y' – 3y = 0, y(0) = - 4, - 4, y'(0) = 0.5 y(t) =

A: The given differential equation is second order linear homogeneous differential equatio. So firstly…

Q: 4/3 5² = 2² -3 (2²) *² y' x

A:

Q: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0 %3D

A: 2x+62y2+3dx+4yx2+3x+2dy=0

Q: D. Exponential shipting Theorem (D°+ 10* - 30 - 18) y = 24 x ° e-s* -3x 4.

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Q: dy 3y Vx +1+x = 0, y(0) =1 dx

A: Explained below

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

A:

Q: Example 4: Solve i) y" + 7y' + 10y = 2x + 3e*

A: the given differential equation isy''+7y'+10y=2x+3exfirstly complementary function CF and then PI…

Q: (15) y "'+ y " =e (16) y () – y (4) = 1 %3D

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Q: y y' + (2х + 3у) = 0 y(x) = ? =>

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Q: Solve: у" + 5у'" — 2y' - 24у — 42е 5t 2y' — 24у 3D 42e — 2, у'(0) — — 6, у'"(0) —D — 30 | | | y(t) =

A:

Q: 2. で-5e dt = 4.

A: ∫xndx = xn+1n+1

Q: Sve SVé -3 dt u = Ve' – 3

A:

Q: a) L{te3t – sint + cost} =? 1 =? b) L-'s-2)(s2+25-5)

A: a) We have to find ℒte3t-sint+cost

Q: y' =xy

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Q: If the solution of y' = 2(2x - y) passes through the point (0,1), determine x when y = 7.

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Q: Solve Xy"-xy' +y = a+3ln(x), y)=Q , yl)=1 %3D

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Q: Solve: y''' – 3y'" – 6y' + 8y = 0 %3D y(0) = – 6, y'(0) = - 12, y'"(0) : - 54 %3D y(t) =

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Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

Q: y'-(2/x)y=(y^3)/(x^2) find the solution that satisfies y(1)=1

A: The given differential equation is

Q: Solve y' = 12xy 2х, у(0) — 15 -

A:

Q: dt' Population growth is commonly modeled upon the simple statement that the popu- lation growth…

A:

Q: hat is y(t)?

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Q: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: 2хуу' — 1 + у? y = 2; x = 1 %3D %3D

A:

Q: Solve y(H) a) Y (6) = y (4) = ? %3D b) y"-y' • 24 ylo)=1;y'(0)=-2 %3D

A: We have to find the solution y(t) from the following  a) y(s)=1s2(s2+1) b) y''-y'=2t, y(0)=1,…

Q: Solve y'"+ 5y' + 4y = 0, y(0) = - 8, y'(0) = 17 y(t) = %3D

A:

Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: (iї) Зx' — 6х %3Dsin2t x(0) = 1 (iv) у" + 6у' + 13у %3D 0 У (0) %3 3, у'(0) 3 7

A: We have to find first complementary function and   particular integral and then add them, that will…

Q: Q3) The component of national economy is as follows: Y= 5000 C= 1800 T= 1400 C= 500+(1/2)(Y-T) |=…

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Q: Solve y" – 6y' + 8y = 3e, where y(0) = 1 and y'(0) = 3. %3D

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Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: x² + 3x + 2 y' = y(1) = 4 у — 2

A: y'=x2+3x+y-2 ; y(1)=4

Q: y' = e2x + y – 1 %3D

A: