7. Solve the following IBVP: Uu = 4uzz, 0 < x < 2n, t> 0, u(0, t) = 27, u(27, t) = 0, t20, u(x, 0) = x - 27, 0

Q: у" — бу' + 9у %3 t'e", y(0) 3D 2, У (0) 3D 17

A:

Q: By cardanos method x^3-6x^2-6=0 is r1=y-a/3 and a=-6 find y

A: Given, x3-6x2-6=0 where x=y-a3 and a=-6. We have to find y.

Q: Given fex) End (f-')'(5) 2X

A:

Q: 47. If S(2,y)=(2x-3yy', then f,= _ a) -15(2x-3y)" b) –10(2x-3y) c) 15(2x-3y) d) 10(2x-3y)

A:

Q: 1) +3)er2+6x dx

A: As there are two questions, first one is solved here.

Q: Solve the IVP, explicitly if possible. 3y x+9(-7)=1 (x– 7)* 8. y=(x+9)3 (x + 9|) yl = (x+9|)

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Q: The critical numbers are x = 4 A) True B) False

A: For critical points we need to put f'(x)=0

Q: 3) S x tari'x dx X,

A:

Q: Zyyy=24x-96y+5 denkleminin genel çözümü aşağıdakilerden hangisidir? O a. z=4x^(2)…

A:

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

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

Q: 5. Find the general solution of the equation _ x² + y² Z (y-x)p+ (y + x)q=

A:

Q: The solution of (1 - y ^ 2) * d * x + (1 + x ^ 2) * d * y = 0

A:

Q: The equation x''+ x = sin t has a bounded solution. true or false ?

A:

Q: 1- yli+zy=2e

A:

Q: Show that the diophantine equation x^4 - y^4 = z^2 has no solutions in nonzero integers using the…

A: To Show: The diophantine equation x4-y4=z2 has no nonzero solutions in integers using the method of…

Q: The derivative of flx)= - 3x -2x? is 5+ 4x

A: Given that -      fx=3x-2x25+4x     f'x=?

Q: The solution of the following Bernoulli's equation y' + 3x²y = 4x²y² is: Oy= 3/(4+3Ce^(x^3 ) ) Oy=…

A: The given Bernoulli's equation is, y'+3x2y=4x2y2. To find: The solution of the given differential…

Q: Find the general solution of the following y^ prime prime prime -5y^ prime prime +3y^ prime +y=0

A:

Q: /x²-1 dx

A: We use substitution and basic trigonometry properties to solve this. Integration may have different…

Q: B) If fx) =-3x² +13 and g(x) =x'+8r-2; find the following. i) (g+f)(x) ii) Ax) - glr) C) 1) If f(x)…

A:

Q: Differentiate the following function: * x2+1 y = -2x -4x y' = y' = (x2-1)² %3D (x2–1)2 Option 2…

A: Differentiate y=x2+1x2-1

Q: 7) 3x +3e'x2/3+tx'=0

A: Given 3x+3etx23+tx'=0

Q: find general solution of (x^2 +y^2 +z^2)p +(x^2 +y^2 -xz)q = z(x+y)

A: Given equation is(x2+y2+z2)p+(x2+y2-xz)q=z(x+y)

Q: 3) f(a) Va +1 & g(a) = & h(a) = Find (fogoh) %3D a+4

A:

Q: 1.J347x2+12x .s 3x2+8x-12 dx

A: 1). Given: I=∫3x2+8x-12x3+7x2+12xdx We know that; ∫1ax+bdx=1alnax+b+C   Note: As per Bartleby…

Q: 4) f(x²+2) lnx dx = a) (+x) Inx--x+c b) (+2x) inx--2x+c c) (x² + 2) lnx--2x+c d) None of the above

A:

Q: The solution of DE.s divided into complementary solution and particular solution. * O True False

A: Consider a nth order differential equation dnydxn+dn-1ydxn-1+dn-2ydxn-2+.........................+y…

Q: 1 Given A= 0 1 0 3 1 0 -3 4 , x = and b - Solve the maxtrix equation Ax = b for x 200 100 250

A: Given  A=1030101-34 , b=200100250 and let x=x1x2x3 Then we have to solve the matrix equation Ax=b…

Q: Solve the IVP dx -5 dt 4 = x (0) = = -4] -5 - x 8 ;] 2 Give your solution in real form. x1 = x2 =

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Q: 3x'e* (x* +1)* 3e a) -+C 2(x² +1) 3e* b) 2(x² +1) +C x? +3 x +1 3 c) +C .2

A:

Q: 7- Differentiate K(x)=(Vx)(5x²+1)³

A:

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5]. O f(4)=0.31,…

A:

Q: 1 4[Vx(ax* + bx +c ]= 2Nx -(5ах* + 3bx + с) b)

A: We have to find  the derivative for the given function