Solve dy (a) dx dy 1+y (b) dx 2x y+1 dy (c) (1+x 2+x dy (d) e*+y

Q: dx (x-1)(x-2) NYC

A: Integrate

Q: dy 3. + y = e3x dx

A:

Q: Dy/dx=(3x-5)(x+1);y=1 when x=-1

A: Given equation is: dydx=3x-5x+1 And the condition is: y=1 when x=-1

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

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

Q: (x - 2y - 1) dy = (2x - 4y - 5) dx

A: Solution:x-2y-1dy=2x-4y-5dxdydx=2x-4y-5x-2y-1dydx=2x-2y-1-52+1x-2y-1dydx=2x-2y-1-32x-2y-1let,x-2y-1=…

Q: Find d³y/dx³. y(x) 2STENTOR x(x-1) 3

A:

Q: d²y dx² 2 (2x-3)² Find y = O O d²y dx² d²y dx² d²y dx² O d'y dx² = = = = 12 (2x-3)¹ -12 (2x-3)4 48…

A: Given equation is y=22x-32. Find the value of d2ydx2. Here we use the differential formulae:…

Q: Solve by separating variables (x-4)y dx-x³ (y²-3) dy=0

A:

Q: d²y - x² = 0 with dx2 (x = -3) = 2, y(2)=4 dx

A:

Q: dy (B) Find -, if dx 3x2 + 2x 2 Y = (- when x = 1 5

A:

Q: d2y/dx2, where y = 4x3/2

A: Given- y=4x32 To Find- d2ydx2 Identity Used- The power rule of derivative ddxxn=nxn-1

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: (2x² + 2xy + y²) dx + (x² + 2xy - y²) dy = 0

A:

Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: (3x + y5)dy – ydx = 0 %3D -

A:

Q: 2x+(4x+y-6)dy/dx=y ODE

A: In this question, we need to solve the given ODE.

Q: Solve: x- dx dy - (x + 1)(1 + y*).

A: First separate the variables than integrate and solve the  differential equation .

Q: 1 2x STAR -1

A: y(x)=1e2x−1dydx=ddx1e2x−1Using the Chain Ruleddxf(g(x))=f′(g(x))g′(x)Using the power…

Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: dy - Find ay for x³ + y²x − 3 = 0

A:

Q: dy dx * = 4y-2 y? 1 y = Ce-4x B A 1 y = Ce 4 A A y = 4x + B y =Ce¯d*+ B A

A: Givne that   The differential equation

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: 2dy+ydx=y3(x-1)dx (Bernoulli)

A: We have to find the general solution of differential equations

Q: Solve 2(ax+Y) dx + (3x +Y) dy =0 ,y) =2

A: SOLUTION-

Q: dy/dx=2+√(y-2x+3).

A: Given differential equation is dydx=2+y−2x+3.......1. We have to find the general solution of the…

Q: y"=? (d2y/dx2) y=2x2+1/x3+2x

A:

Q: (x+y+2) dy dx dz

A: The given integral is: ∫-11∫-11∫-11x+y+zdydxdz

Q: x³ dy + (3x²y - xe* + ex) dx = 0

A: The given differential equation is; x3dy + (3x2y-xex+ex)dx =0

Q: ydx + 2(y4-x)dy=0

A: