2. [e²v ycos (xy)| dx + [2xe2y (xy) + 2y] dy = 0 xcos - -

Q: 1. Test for exactness and find the particular solution of dx + + dy = 0 (1 – xy)? (1 – xy)² |

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take…

Q: 1. Classify the D.E. 2xe dx + (x²e + 1)dy 0.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: 4. (ye"-2y)dx + (xe-6 xy- 2y)dy = 0; x = 0 when y = 2. 5. (x+3) cos y dx - (sin y In(5x + 15)-y} dy…

A: The exact differential equation for the equation, F(x,y)=C, is written as Fxdx+Fydy=0, where, Fx ,…

Q: 2. (e2y – y cos xy)dx + (2xe2y - x cos xy + 2y)dy = 0

A: Exact differential equation

Q: 1- xy dy + (x² + y² )dy = 0 dx 2- 2. dy – y = ex/2 3- (x + 2y)dx – xdy = 0 dy 4- cosh x+ (sinh x)y =…

A: As per the guidelines we can solve 2 problems.

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: If z + In(e2x - e + e²) = 0 dz find at the point (0, 0) dx 2 0 -3 -2

A: see below the calculation and answer

Q: (y² cos x – 3.x²y – 2x)dx + (2y sen x – x° + ln y)dy = 0, y(0) = e

A:

Q: 6) Solve the homogeneous differential x2 + y? dy quation dx 2xy

A: on solving this we get

Q: 1 Let y = -. Find dy and Ay at.x = 7 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

A:

Q: Hello! Can you help me with this calculus problem?

A:

Q: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

A:

Q: 2. [sin y -ysinx]dx+(cos.x+xcos y+2y)dy=D0 (4x°y-4xy)dx-(x-x dy D0 3.

A: Given that: (y2+4x2y-4xy)dx+(x2-x3)dy=0

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

A:

Q: 1) (22 - ry + y?)dx - xydy 0, where y(1) = 0

A:

Q: B. (y + e*seny)x + (x + e*cosy)dy = 0

A: The differential equation is given as  y+exsinydx+x+excosydy=0 Compare it with Mdx+Ndy=0 to obtain…

Q: Solve the D.E [y(++csy)]dx + [x+Inx-xSiny] dy-o

A: Solve de

Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

A:

Q: 2. [ey ycos (xy)| dx + [2rev xcos (xy) + 2y| dy

A:

Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

A:

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

A:

Q: (4 + e² ë*) dx + (1 +et) dy.so *) dy so A Scanned with

A:

Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

A:

Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

A:

Q: Q2. Solve y [xcos (e)- + ysin (:)] dx – x [ysin 2) – xcos (2)] dy =

A:

Q: Find the differential dy of the given function. y = √x +1/√x

A:

Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS

A:

Q: {[1+ y²] sin(xy) + xycos(xy)}dx + {[1+x²]cos(xy) – xysin(xy)}dy=D0

A: Given     1+y2sin(xy)+xycos(xy)dx +1+x2cos(xy) - xysin(xy)dy=0

Q: 4) (у-сos' x) dx + cos xdy %3D0 5) 2y(y² - x)dy = dx

A:

Q: Find the differential dy of the given function. y = V 3 - x2 dy =

A: Find derivative

Q: 2x = - (x2 + y²) (1 + 2 e) dx + 2 e7(1 -5 dy = 0 x = y In y-y In x dx O (y? – x2) dx + xy dy = 0 O…

A:

Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

A:

Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: 25. (y cos x + (2y sen x – xr + In y) dy = 0, y(0) = e 3xy – 2x) dx –

A: The given differential equation is: y2 cos x - 3x2y - 2xdx+2y sen x - x3 + ln ydy=0  ;…

Q: 1. + e*y² = x²y² dy da 2. y + sin x = x³y 3. In x - x²y = xy dy da + cos y tan a

A:

Q: 2y dx = 3x dy Xy dx + ex t xp, hx dy= xydx 2 3 O Xy'dx+ (y 1)e dy = cos x casy レ

A: 2.xy3dx+ex2dy=0

Q: The equation (y-x)=x(dy/dx) is Bernouli (y^n> 1) O linear in x O Homogenous O variable separable

A:

Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

A:

Q: 1. Determine the general solution of (x 3y )dx – x dy = U

A:

Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

A:

Q: Find the differential dy of the given function. Y=x+1/3x-2 Dy=?

A: Given, y=x+13x-2

Q: 3) Find dy/dx Cas %3D X-

A: Given:

Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: Find the value of the differential dy for y = e7x + 2x if x = 0 and dx = 0.1.

A: d/dx(e^(mx))=m e^(mx)

Q: Find the value of the differential dy for y = e3x + 5x if x = 0 and dx = 0.1.

A: We know the differential dy of  y=f(x) is given by, dy=f'(x) dx

Q: Test for exactness and find the complete solution of dx + [ In 2(x-1) + dy = 0 х-1

A:

Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5