dy 4) 2xy = x² + y? + 1

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: oS% (x? + y? + z*) dz dy dy

A: Solve the following

Q: NOTE: Enter the exact answer. yz dx dz dy %3D -144 –96

A:

Q: For yx + 2x + cx = 9 ,m = 3,Find c at (3,1)

A: Given y2x+2x+cx=9 . m=1. We need to find c at (3,1).

Q: Given a = 5t – 30 and y = 25 sin t dy (i) da dy (ii) dr?

A:

Q: Solve the following aifferen tial equations |. x* dy = (4x* +5xy +y*) dx 2 2x + y X -24 2. dy dx

A:

Q: (2xy tx?+x*) dx - (Itx²) dy=D0

A:

Q: I need help to find particula solution using undetermined coefficients: y''+4y = sin(t) + t2 + et

A:

Q: Use the substitutions : = ye S =X Q.3 to solve the du + y Əx PDE : %3D х, и(1, у) — сos y.

A: Using the substitutions we will solve for the PDE given as follows: ∂u∂x+y∂u∂y=x ∂u∂x+y∂u∂y=x…

Q: In the given Bernoulli's equation 6y²dx – x(2x³ + y)dy = 0, what is ƒ P,(y)dy?

A: I have appended the formula used in the solution part

Q: NOTE: Enter the exact answer. yz dx dz dy -180 J–120

A:

Q: Find a solution of x dy =y?-y that pases du Through indicated points

A: For the given problem, below is the solution.

Q: y²dy = x(xdy – ydx)ey

A:

Q: Solve the following DE: (1+ )S'+2St dS *where S'= dt

A: This question is based on solution of 1st order differential equation.

Q: -dz , where y is given in the figure z2+1

A:

Q: Given a = 7t – 15 and y = 49 sin t dy (i) dr dy (ii) dr?

A:

Q: Given f(r, y) = 6e2 sin(4y) then V

A: For the gradient calculator firstly we differentiate partially and then put the value of x and y…

Q: To which coordinate axes are the following cylinders in ℝ3 parallel: x2 + 2y2 = 8, z2 + 2y2 = 8, and…

A: The cylinders x2+2y2=8, z2+2y2=8 , and x2+2z2=8. We have to find to which coordinate axes are the…

Q: Use appropriate substitution to solve the following (iv) zy" + (y/) 0. %3D

A:

Q: Find the GENERAL SOLUTION. 1) ex-ydx + sin y sec x dy = 0 2) y(u? + 1)du + (u³ – 3u)dy = 0 %3D |

A:

Q: Solve the given DE. (D² – 3D + 2) Y 1 cos² (e¬²)

A: Differential equations, method of variation of perameters

Q: Use the correet fransformation to Find the solution of the Problem below. 一00<Xく00 0< Y<1…

A:

Q: Without solving, classify the following equations as to: separable, homogeneous, exact, linear,…

A: Classification of the differential equation

Q: Solve the following diffential eauations a) dy + 4 y = e dy 3n2y = そ? ea3 dy C) N + 2y = そマ dn

A: We need to solve DE.

Q: Given z = 6t - 45 and y = 36 sin t dy dr dy dz?

A:

Q: NOTE: Enter the exact answer. (36–z² xy dy dx dz

A:

Q: dy 5. If y = e3+1 sin(1 – a²), then Find da

A: We have given y=e3x+1sin1-x2 We have to find dydx.

Q: Use the d'Alembert solution to solve 1 0u 9 dx2' u(x, 0) = cos? x, u(x,0) = e"+1. -0 0, t > 0,

A:

Q: Show if the following statement is true or false. If it is true, write TRUE. If it is false, write…

A:

Q: (х — 2у)dx + (у — х)dy %3D C

A: Given differential equation x-2ydx+y-xdy=0 It is of the form Mdx+Ndy=0 Here, M=x-2y and N=y-x…

Q: Given a = 12t - 31 and y 144 sin t %3D dy (*) 12cos(t) %3D da (6) da?

A:

Q: If y = u³ - 2u + 1, where u = 2√x, find at x = 4 -23 23 33 none of the above dy when x =

A:

Q: Solve the following and show the complete solution. Find D,f at P: f(x,y) = sin(8x – 5y); P(5,8)); u…

A: Given,            fx,y=sin8x-5y ; P5,8 ; u=35i-45jTo find : The directional derivative, Duf at P.

Q: Solve the diferential eguation with discasfssic Of soaL (4xy-y2) dx +(2x? - 2 xy + 2y?) dy=o

A: Given the differential equation is 4xy-y2dx+2x2-2xy+2y2dy=0 This is form exact differential equation…

Q: Given r = 15 In(t) and y= 225 t then find dy dx d'y da?

A: Given that x=15lnty=225t2

Q: Solve the following DE 3 X dy %3D

A:

Q: 7 dy (18a* + 16e5)', find da Given y = %3D

A: It is given that,

Q: 5. (1+ y² + xy²)dx + (x²y+ y + 2xy)dy = 0

A: The differential equation is given as 1+y2+xy2dx+x2y+y+2xydy=0 Compare it with Mdx+Ndy=0 Here M =…

Q: Solve the DE by Method of Undetermined Coefficients y" +5y +4y = 90 sin 4r y (0) = 1, y (0) = 2, y"…

A: Given that y''''+5y''+4y=90sin4x Now take the homogenous term, y''''+5y''+4y=0 Take m=ddx,…

Q: Given * = 11t – 25 and y = 121 sin t %3D - dy (*) da dy (é) da2 ||

A:

Q: Solve the following 3. y* Va - y* dy

A:

Q: Solve the following problem %3D 0, 0 0, + dx² ' ay? u(0, у) —D 1, u(п, у) %—D 0, и(х, 0) %3D 0, и(х,…

A:

Q: 8 sin r at the point (, 4). e form y mx + b where

A:

Q: Given a = 12t -31 and y = 144 sin t dy (*) 12cos(t) da dy (6) da?

A:

Q: dy dr 4 - y (b) _ In(교2 + y? + 1) dr dy (a)

A: Evaluation of the double integral

Q: Solve the following IVP: dy sin(z*)e %3D dx y(2) = V5 %3D

A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…

Q: C. Given that y = e* sin x, show that d?y +2y 0

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.