7. yy" + (y')² + 1 = 0

Q: tx' 3 - - (³ 4) X X = C1 (1) +02 10 + ()

A:

Q: 12e* y' - 2y'+ y = 3

A:

Q: 4/3 5² = 2² -3 (2²) *² y' x

A:

Q: 5). § sech x tanh-x dx

A:

Q: 5. fx³ cosh¯¹(x²) dx

A:

Q: (2) Find it -ソ= x(lue) 2- Y=lu(Cosx )

A:

Q: 4y'''+12y''+13y'+10y=0

A:

Q: x' = 2 -5 1-2, X

A: We will find eigen values and eigen vectors of coefficients matrix from given system and then find…

Q: 3. y' = 3x? –2; y(1) = 5

A: When the linear differential equation is in the form, dydx+py=Q    ..........1 Then the solution of…

Q: 9. y" + 2y'- 3y = 1 + xe*

A: The given equation is; y''+2y'-3y=1+xex.

Q: x²y' = 4x² + 7xy + 2y²

A:

Q: 13.9y" +12y + 4y = 0, y(0) = 2, y'(0) = -1

A:

Q: (x²-ax +4" dx

A:

Q: x²dx х2—4

A:

Q: y''''' - 3y'''' + 3y''' - y" = 0

A: To solve y""'-3y""+3y"'-y"=0

Q: Find y'' in y = (1 + 1/x)3

A: We first expand the given expression first.

Q: X+3 Evalmating dx 5-4メ-メ2

A: We have to find the integral of given function.

Q: 16. y" — у = 0

A:

Q: 11. x² +1 Find +3x+1 -dx

A:

Q: 7) | sec x. dx

A: Given:       ∫ sec5x dx

Q: 8. x' x, x(0) = - (-³)

A:

Q: y"+y=sec³x

A: The given equation is: y"+y=sec3x

Q: y''''' + 8y''' + 16y' = 0

A: Given differential equation yV+8y'''+16y'=0 We have to find the general solution of the given…

Q: 36. y' = y/2 %3D

A:

Q: 45. y' - 2xy = 0

A:

Q: 6. (D² + 1)y = 10e* sin x

A: see below the answer and explanation

Q: 9. y"-2y+3y=0

A:

Q: X dx 2-1

A:

Q: 5. Use 2- step substitution tan 4x sec² (4x) dx

A: To solve the integration

Q: 5. x' -1 - = × 2 -3,

A: Given: x'=-1-122-3x  …………………………(1) To find : The general solution of the given system of equations…