(ry +y ) y' = y?. y' = エーリ+3 y' =

Q: au au = xt at (x > 0,t > 0) ax u(0, t) = 0 u(x,0) = 0

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Q: 6. 7. 8. dy x- -= x² + y y = x² + 4x; dx In y = C₁e* + c₂e-x; yy" - (y')² = y² In y y−³ = x³ (3ex +…

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Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: dy - 2y + 6 Find the solution of the differential equation. - dx 2.x + y + 2 ||

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Q: y" +9y' = 9 tan 3x

A: The solution is given by using method of variation of parameters as follows

Q: Solve the differential equation. dy = 5x* e -y dx

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Q: (e"siny + tany)dx + (e*cosy + xsec*y)dy = 0

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Q: 4xi4=*

A: Order :-The order of a differential equation is the order of the highest order derivative involved…

Q: c) (y')Va? - 16 = 11x d) yy -10e2t = 0

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Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

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Q: y" + y = secx tan x

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Q: x" – 4x' + 4x = et a. x = et b. x = e2t c. x = e2t + et d. x = te2t + et а. С. e. x = e2t + tet

A: Given : x" - 4x' + 4x = et

Q: (x² + 2xy- 4y?)dx- (x² – 8xy– 4y²)dy=0 | O x² + 4y² = C(x + y) O x2 +y2 = C(x+ 4y) O x2 + 2y? = C(x…

A: Solution(x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0dydx=x2+2xy-4y2x2-8xy-4y2(∙)this differential equation is…

Q: du х — у— 1

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Q: dy xy' = 6y + 12x*ys, (y' = dx

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Q: 3 2 7. ty'-2y=t³ sin(2t) − t³ +4tª; y(n)= · Use a graphing utility to draw a graph of the solution…

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