Q10. If f(x, y) = cos( 3x + y) Find:

Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

A:

Q: 1. Given f(x, y) = e sin(x² + y² ), find -2x and ôxôy ôyôx

A: Given: f(x,y)=e-2xsin(x2+y2)

Q: dy 7. dx cos(x + y), when x = 0,y = 4

A:

Q: H.W Find y' for y = e©osx * tan¯'(5x) * (5x² + 1) ?

A:

Q: Q7) If y = tant ,x = tan?t at t = -! Find by using Chain Rule dx

A: We have to find derivative

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: Q2 Find (d y/d x)& (dy/dx?) y 1/ cos xy ex =

A:

Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

A:

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

A:

Q: O XsinCyldx +(x^t)cos(y) dy=0

A: We have  xsinydx+x2+1cosydy = 0  x2+1cosydy=-xsinydx cosydysiny=-xdxx2+1

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy %3D

A:

Q: Q4: Find dy\dx if|cos?y +5y2 = x2

A:

Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: If f(x, y) = x cos y + ye", find dydx

A:

Q: Q4) If g(x, y) = x²y + cos(y) + y sin(x) Find gxx, Iyy 9xy, Iyx

A:

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

A:

Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

A:

Q: Q;: Find for the following functions: - dx xcos (x³+1) 2- y = Tx cos" (x³+1)

A:

Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: Q2 Given z = xw? + cos y + wx , w= t , x = 2t2 , and y = 3t, find dt

A:

Q: Q4: Find by using udv method cos bx dx ax

A:

Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

A:

Q: Q4) If g(x,y) = x²y + cos(y) + y sin(x) Find gxxgyy, 9xy Iyx (2M)

A:

Q: Q3: Given f (x) = sin(x) cos (2x) and h = 0.5, find (numerically): Sf(x)dx а- b- f()(2)

A:

Q: Given f(x, y) = 2e" sin(4y) v (0, then V %3D 2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Q4) If g(x, y) = x²y + cos(y) + y sin(x) Find gxx, Jyy» 9xy, Iyx (2M)

A:

Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find fy(1,2,0). Leave your answer correct to two decimal…

A:

Q: y" – 4y' + 4y Cos 4x -

A: The given differential equation is y''-4y'+4y=cos4x ...................................... (1)

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

A:

Q: = cx + In(cos x). For what value of c is f'(T/4) = 7? C =

A:

Q: f(t) = e¯3t cos ( at + cos ( 2at + 3 2

A:

Q: Suppose z is a function of x and y, and tan Vy? +x² = ze6y. Solve for and dx ду

A: Here, given that z is a function of x and y and tan y2+x2=zxe6y⇒tan y2+x2=ex ln ze6y...(1)

Q: Given f(x,y) = ex cos y, Evaluate fy(2,0) O e² cos 2

A:

Q: Q3.If f(x,y)=sin(x-3y) + sin(x1 find: af 2x and af dy

A: We can find partial derivative with respect to 'x' and 'y' .

Q: Q2:B/ Find dy/dx f Via - "sin Vi dt y = + cos t dt

A:

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

A:

Q: Q2 Find (d y/d x)& (dy/dx?) y 1/ cos xy ex %3D

A:

Q: Suppose z is a function of x and y. and tan Vy? + x² = 2"e6y dz dz Solve for and

A:

Q: (e) y' +2y : = cos(2x)

A:

Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

A: Partial derivative of a function of two or more variables with respect to one variable is the…

Q: Find fur for f(x, y) = 7xe* y° sin (/x - 3x* +1)+9x°e"

A:

Q: dy 7. dx = cos(x + y), when x = 0,y == 4

A: Differential equations, with substitution method and separation of variables

Q: H.W Find y' for y = ecOS X + tan-(5x) (5x2 + 1)?

A:

Q: Q2 Given z = xw? + cos y + wx , w =t, x = 2t? , and y = 3t, find dt

A: Let's find.

Q: What is general solution of the given ODE. * dy cos? (x – y+ 1) dx .2 COS

A:

Q: (i) f(t)= est+cos 4t

A: According to company's rules, I need to solve first question when multiple questions are posted...…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.