The general solution of differential equation D'y= Dy is Ge b) +ce* b) c;e* +cze* c) d) O c) Ob) O a) d)

Q: It is known that yı = e¯* is a solution of the differential equation y' – 2e* + 4y – e"y² = 0. Find…

A: Note: The given equation y'-2ex+4y-exy2=0 is incorrect as the solution y1=e-x does not satisfy it.…

Q: Consider the differential equation (D² – 1) y = e* + 1. What is y, ? A y. = c, + C,e + C, e* ® . =…

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Q: 园 Test Yourself 01 Solve the following differential equations: (Bali, 2007) 1) e-Ysec?ydy = dx + xdy…

A: 1) e-y sec2y dy = dx + xdy 2)yey dx=(y3 +2xey )dy 3)dy/dx =y/(2ylny+y-x).

Q: 7) What value of N(x, y) will make the differential equation (3r2y +422)dr + N(x,y)dy = 0 exact? a)…

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Q: Which of the following is the Euler (Cauchy) differential equation whose general solution is y =…

A: In this question, the general solution of the Cauchy  equation y=c1cos(lnx)+c2sin(lnx) It is…

Q: In solving differen tial equation system dy + 3z = 0 dt y = ? – 3y = 0, dz dt A) y = C, cost + C2…

A: Given: dydt+3z=0dydt-3y=0

Q: 1) When changing the variable u? = 4x + Y The differential equation 4x + y dx – x dy = 0 Becomes: du…

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Q: dy + 3x- dx The degree of the differential equation y- dy = 3 d'y + is dx dx? а) 3 b) 2 c) d) None…

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Q: Transform the equation y + (ar - v + by = 0; y = Vau(x) Use given substitution and show that above…

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Q: dy Y+2 dx y(1) = 5 → y(e) = ? (use y=ux substition) A) e B) 3e C) 5e D) 7e E) 9e

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Q: dy a) = cotx cot y dx b) (x² + 1) dy dx = xy² + xy = c) (1 + x)2 dy dx + y² = 1

A: Let us consider a differential equation of the form dydx=f(y)g(x) Then the differential equation is…

Q: We can transform the equation y'+x3y=(sin(x)/sqrt(y3)) to a first order linear differential equation…

A: Given equation is: y'+x3y=sinxy3

Q: 17.) Keeping r as the independent variable, make the substitution u = y in the differential equation…

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Q: Which of the following differential equations can be solved by utilizing the method of undetermined…

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Q: The order and degree of the differential equation A) 2 and 4 B) 3 and 4 2 and 3 D) 3 and 2 d²y dx2…

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Q: a) Show that y = C,e-2x + C, e-3* is the solution for the differential equation y+5y'+ 6y = 0, where…

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Q: a) y -y = e*y?

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Q: c) Show that y, = x* – x² Inx over the interval (0, 0) is the particular solution to the…

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Q: Solve the first-order linear differential equations. a) x+2y= 1 - 1, x > 0 x

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 5. For the non-homogeneous differential equation x²y" – 4xy' + 6y =2x* + x² a) Show that x2, x3each…

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Q: State the order of the given differential equation. (1-x) y" - 4xy + 5y = cos x d³y +y=0 dx³ a) b)…

A: a) The given differential equation is (1-x)y''-4xy'+5y=cosx. Since y'' is the highest order…

Q: d*y dy is dx x dx ferential

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Q: b) Form the differential equation from the function x = Acos(nt + a). e) Given that y = eax sin bx,…

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Q: a) 1" – 3y + 2y = 4x² b) y" + 2/ + 5y - 6 sin 2x + 7 cos 2x c) y"+ 2y + 4y = cos 4x

A: Thanks for the question :)And your upvote will be really appreciable ;)