Find the general solution 1. (D? – D - 2)y = 0

Q: ² - x ²² = y² dz ४x d²z Find the solution of xy' буду

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Q: dy Q3. Solve the DE da +y - y? provided that y1 = - is one known solution of the equation.

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Q: The general solution to D. E 2y(4) – y'"" – 2y" + y' = 0 - is given by y(x) =

A: The genaral solution to D.E2y(4)-y'''-2y''+y'=0

Q: d²y - y = у 3 10sin?x %3| dx2

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Q: (x+xy²)dxte*, ydy=D0

A: Given: x+xy2dx+ex2ydy=0 ⇒x1+y2dx+ex2ydy=0 ⇒ex2ydy=-x1+y2dx ⇒y1+y2dy=-xex2dx

Q: A. Obtained the general solution. E... 10. (D² – 3D + 2)y = 3x²

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Q: 2. Use the mothed of variation of parameters to find the general solution of the following…

A: We can solve this using variation of parameters for three variables

Q: 6. Find the solution of dy = (y² – y)x². dr

A: Definition used -          The solution of the variable separable differential equation-…

Q: The solution of (D² – 4D+13)y 0 5 2x (A eix . Be Jox (A ex + Be)

A: D2-4D+13y=0 The auxiliary equation is m2-4m+13=0 ⇒m=4±-42-4132⇒m=2±3i

Q: The solution to y + y = 0, y(0) = 1 is positive for all z e R. 14e

A: Given initial value problem is

Q: Find the solution for t> 0. Note that you can assume yı(t) = t". t'y" – 3ty' – 12y = 0

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Q: For the solution: y(t) = C1e-t + C2e5t solve the IVP. First for: y(0) = 1 and y'(0) = 0 Second…

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Q: Solve the following equations by two methods: (a) using reduction of order, (b) using variation of…

A: Reduction of order is a technique in mathematics for solving second-order linear ordinary…

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: 5. (D² + 4D + 4)y = 0 ;when x = 0,y = 1,y' = -1

A: Given equation is, D2+4D+4y=0, x=0, y=1, y'=-1 Now, write the auxiliary equation for the given…

Q: dy Q(4) Find the general solution of = (r – y + 5)2. da

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Q: OBTAIN THE GENERAL SOLUTION (y? - - ) 1. 3 y + (2 y - 3) dy = 0

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Q: Solve the given DE. (D³ + D² + D+ 1) y = 0 ; y (0) = 2, y' (0) = 2, y" (0) = -4

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Q: x² + y)dx + xy dy = 0

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Q: (c) Solve the difference equation Yt+2 – 4YŁ+1 + 4Y; = 2(2*) + t² - Given initial values Y, = 2 and…

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Q: dw 4w A) Give the general solution of dx = x³. B) Solve y' + = y²x³.

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Q: Find the values of "r" for which y(x) = e* solves the equation y" +3y'-4y= 0

A: We have to find the value of r .

Q: (b) Solve y" + e*yf + (1 + x²)y = 0, %3D x = 0, if y(0) = 1; y'(0) = 0. %3D

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Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

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Q: Q-1:B: Solve the initial value problem d?y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 %3D %3D dx2

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Q: Solve the following equation for c: 1 2-c-z 2-²-y 1 dz dy da 10

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Q: Obtain the general solution unless otherwise instructed 3. (D² – 3D + 2)y = e2*(1+ e2x)¯1 SUMMARY OF…

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Q: Find the solution to the Bernoulli Equation. 2x³y = y(y? +3x?)

A: The solution is given as

Q: What is the solution of the DE xdy – ydx = x2 dy? A. y(1- x) = xc В. (1 - у) %3 хс С. у(1 + x) %3 хс…

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Q: Find the particular solutions of the following equations: dy 4r +y given y-4, when x=1

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Q: Find the particular solution. (D^2 − 2D − 3)y = 0; when x = 0, y = 0, y′ = −4

A: From the given differential equation; D2-2D-3y=0 The auxiliary equation is: m2-2m-3=0 Now solve;…

Q: Q4/ solve the following equations. d²y dy + 81- = 0 dx² dx

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Q: The solution of D.E " -y = 5(t – 1) ,y(0) = 0,y'(0) = 0

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Q: (D² – 3D + 2)y = e2*(1+e2x)

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Q: d*y d?y 4. dt2 24 dt4

A: Given differential equation can be evaluated as shown below

Q: Q(2) Find the general solution of (2r2 + y)dr + (x2y-r)dy 0.

A: Solve the differential equations using exact differential equation method

Q: Solve the he (D’+ 4D+4)y(x) = 5e equation y,)-(2x+1)e - y,) (2x+1)e y,(x) (2x-1)e 32

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Q: dy (x² + xy) = 3xy+2y² In solving , one sets y VX. Which one of the following equations are then…

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Q: 1. Find the general solution of the equation By - ty 11 y t

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Q: Q(5) Find the general solution of (r+2y- 4)dr - (2r +y- 5)dy = 0.

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Q: Find the general solution of the following: 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D² – 5D) + 4y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: C. Find for the general solution of the following DE. 8. (D3 + 3D2 – 4D)y = 0 9. (DA + 6D3 + 9D²)y =…

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Q: The solution to the equation is ged (D²-D-6)y(x) = xe %3D 1 1 1 e* (5x + 2) -7 y,(x) = - t xe" (5x +…

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Q: Y2 = Y1(x) / "dx (5) as instructed, to find a second solution y,(x). у" - 8y' + 1бу %3D 0%; Y1 = e…

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Q: Find the general solution of the equation 4y'' + 4y' + y = e-t/2

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Q: In obtaining the solution of xy2dy – (x³+y³) dx=0 when y ( 1) =0, what is the value of C? (A) 2 B 1…

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Q: 3. Find a second solution to y" – 25y = 0, given one solution y1(x) = e5z. %3D %3D

A: Given differential equation is y''-25y=0 & y1x=e5x be one solution of the differential equation.…

Q: Solve the diffedential equation 2 e ys + y de ]dy-o

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.