Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then W(y1, Y2)(4) = (A) 3 vē (В) Зе (С) 3 (D) ? (E) None

Q: 5x Differentiate y= (4x – 3)* * 4x + 1 y' = (4x – 3)5 -60x – 15 y' = (4x – 3)5 - 15x + 1 (4x – 3)5 |…

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Q: Solve the pollowing: り ( 2+J(xtjy) X=? ye! (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)-2j x=?…

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Q: For the difference equation given by y(k +2) - y(k + 1) + 2y(k) = 2* with y(1) = y(0) = 0 Find the…

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Q: 5. Solve the equation * SHOW YOUR COMPLETE AND CLEAR SOLUTION. (»^)² + (x – 2x+ ) y' +x--xt = 0 |…

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Q: If y' = х-у then its solution is x+y'

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

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Q: Solve the pollowing: () (^) 2+j =j(xtjy) X = ? y=? (1) (2+j)(3-j2) = a+jb () (x-j2y) -(y-j«)-2tj a:?…

A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy…

Q: 3. Find the general solution of 2ху? + 4 %3D 2(3 — x?у)у'. А. X2у2 + 4х — бу %3D С B. x²y? – 4x – 6y…

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Q: (C) y" + 21y+8x=y" + 5y' + e²*

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Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

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Q: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

Q: 3. y' = 5y + e-2*y-2 y(0) = 2 У (0) - 4. хуу' + 4x2 + у? 3D 0 о у(2) 3 —7

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Q: Which of the following is the solution of ди +2- ди Ox 0 = a) u(x,y)= e"-2x b) u(x, y)= (2x + y)³ c)…

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Q: the associateu mCs are paamei. 6. Find the DE of y = ax2 + bx + c by eliminating the arbitrary…

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Q: If r(y) = e³y² +3 find r'(y) =

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Q: 1 — х x(х + 1)

A: Inequalities

Q: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

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Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = + 10e',…

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Q: C. 6y = 3x3 – 2x² + x + 6e¬x? y' = x³ – 2xy when x = 0, y = 1 B. 4y = 2x2 – x + 3 + e¬*² A. 2y = x2…

A: Given y' = x3-2xy when x=0, y=1 y' +2xy = x3  Formula: ∫ex dx=ex∫xndx =xn+1n+1 For the differential…

Q: (3) y "'- 2y "– 4y '+8y = 6xe²* %3D

A: Note: " As per our guidelines we will solve only first question . If you want any specific question…

Q: 7. Find the general solution: y(x? + y²)dx + x(3x² – 5y²)dy = 0 a. y³(y² – x²) = cx b. 2y3(у2 — х?)…

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Q: For the difference equation given by y(k + 1) + y(k) = 3 (1/2)* with y(0) = 1 Find the expression of…

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Q: b) y(4) + y(3) – 7y(2) – y' + 6y = 0. c) y(4) – y(3) – 7y(2) + y' + 6y = 0.

A: Solve the given differential equation Here I am giving answer of 1 st problem if you want answer of…

Q: If r2+ 2r –1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients,…

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Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

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Q: y=cJ,(/2x) +c,J,(/2x)is solution for x?y "+xy'+ (2x² – 4) y=0

A: Given, y=C1J42x+C2J42x is solution for x2y''+xy'+2x2-4=0 To find that this statement is true of…

Q: - 2xy³ + y² + (xy³ – 2y)y' = 0

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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.