ut + yux - xuy=0, u(0, x, y) = e(x-1)² – (y−1)²

Q: Find y as a function of a if y(0)2, y'(0) = 3, "(0) = -13. y(x) = y″ − 4y″ − y′ + 4y = 0,

A: Given a differential equation:initial conditions are:

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: x2y3-y=x+x2 find dy/dt

A:

Q: If y = Vx? – 2x then y' 2(x-1) 3x2-2x %3D

A:

Q: y = (x² – 1)lnx

A:

Q: Find F′(x).

A: Given Data The integral function is F(x)=ꭍxx+2(4t+1)dt.   Solve the given integral function,

Q: ' (x² +2)+4x(y² +2y+1)=0, y(0) =1.

A:

Q: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

Q: dy y = x-'(a² + x²)¿, solve for dx

A:

Q: Find y as a function of x if y(1) = 1, y'(1) = 4. y = x²y"-7xy' + 16y=x6,

A:

Q: 1+vx [8] Find y" of y =

A:

Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

A:

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: Solve the ODE  y'+(1/x)y-ex=0, when x>0

A:

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

A:

Q: Solve the nonlinear ODE Ay''+Byy''-y=0, where y=y(x) and A,B are constant

A: The given nonlinear ODE is: Ay"+Byy'-y=0 where y=yx and A,B are constants.

Q: x(3-5x) 2. dx (3x- 1)(x – 1)²

A:

Q: ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A: We will first check whether given equation is exact or not ,then we find general solution…

Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

A:

Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

A:

Q: Answer: y = -(e-x + c)/(1 + x2)

A: Given differential equation is,

Q: y (2 xy +1)= xy'

A:

Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

A:

Q: dx xy dy x² + y² Ans. y² = 2x²ln (

A:

Q: Find y': Vä+1 VI+1 .2 %3D

A: Answer and explanation is given below

Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: 2. +x +1 d

A:

Q: If y= X 1-x +7x+9, find y' .

A:

Q: xnx Find y'. y =x *m

A: Given, The equation is y=xxln x.     To find: y'

Q: xy5 = zy"+yx²

A:

Q: Find y as a function of if y(0) = 2, y'(0) = 9, y'(0) = -58. y(x) = y"-4"-y + 4y = 0,

A: We are given the homogeneous differential equation: y"'-4y"-y'+4y=0 and y(0)=2, y'(0)=9,y"(0)= -58.