Q3: Given T(u) = sin (u), where u = /x2 + y2, find T- Ty. %3D

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

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Q: Q4: Find the value of for the expression y = e* sin (x) at x = 0. dx

A: To find dydx at x=0

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: Given y= sin3x, dy at a = 3 is approximately

A: The given function is y=sin3x. Differentiate the given function as follows. dydx=ddxsin3x=cos…

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

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Q: f(e) = Given r2 + 14x + 40 dx 1+ cos2 (x) At what value of t does the local max of f(t) occur? %3D

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Q: 7 Cos X dx e 4 Using the Midpoint Rule, M(50) =| |: %3D

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Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

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Q: Hiw Solve y=Jx+y' for X=oco.2) 2 by given Xo=0,9o=0· Rung Kutta methood Por 0.0.E (first ordey)

A: Runga Kutta First order method is also known as Euler's Method.

Q: Q3 Integrate using trigonometric substitution: dx I To +x² /9 +

A: Let (x/3) = tant Differentiate on both side  dx/3 = sec2t.dt dx = 3.sec2t.dt

Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

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Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: 4 dx 1+ By using (Answer one only) a- Trapezoidal rule when n=5 b- Simpson's rule when n=6

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Q: +00 1 1 : dx x[In(mx)]3 m+3 8

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Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

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Q: 4. Find . d?y of the functions x = 1+ cost and y = 1– sin t. dx2

A: Differentiating given parametric equationswith respect to t,x=1+costdxdt=-sint…

Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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

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Q: dy Consider the IVP dx (2y – 3x)?, y(0) = 0.

A: Consider u as 2y-3x. Differentiate both sides of the equation u=2y-3x to obtain the expression of…

Q: Q3: Find the general solution for the following Deferential Equations using d?y + y = sin x…

A: Given differentiatial equation is solved using Variation of parameter method.

Q: 些。x? dx z + 6 -4 y %3D хе ? dx4 with YLoI = 5,y'col =1, 9°co) --2 yiol e 007

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Q: Q4: Find for the following functions: - dx 1- y = 2cot? xcos (x3+1) x cos² (x³ +1) 2- y =

A: Given functions are 1) y=2 cot2x-1x+1 2)y=x cos2x3+1x cos2x3+1 We need to find differentiate of…

Q: -T/2 Q4: Evaluate e sinx dx by using trapezoidal rule so that er < 0.025.

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Q: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

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Q: Q1-lf x= cot- VE. y= find at t = 2.

A: Given: x=cot-1t and y=1t+1

Q: Q4: (etan 3x) (sin-12*) (2*) vsinh x+4 A) Find for the following functions: y = dx

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Q: (a) Use n = 6 subdivisions to approximate the value of 6 Vx + 3 dx by the trapezoidal rule.

A: We need to find approximate value by trapezoidal rule. NOTE - AS PER OURGUIDELINES WE CAN NOT SOLVE…

Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

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Q: cos(x) dæ with n = 4 is: The Trapezoidal Rule approximation for

A: Given ∫14 cos(x)x dx   n= 4 here f(x) =cos(x)x

Q: Q4: Find dy\dx if|cos'y +5y? = x?

A: The given equation iscos2y+5y2=x2to find dydx

Q: f sinh3³ x dx Ocosh³z-coshz+C O3 cosh³r+C 3 Ocosh³z + cosh 2+ C Ocosh³ +C O None of the choices

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Q: 1 dx using the trapezoid rule with n=4 1+x d. Use your answers for parts a and b to estimate

A: Given the integration ∫0211+x3dx

Q: I"y= sin?t+ tant, x=- In(- cost)– e sinr, find the value of y whent=". 4

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Q: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

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

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Q: (b) Solve the following initial vahue problem by separation of variable = 2x at x = 0, y=-2 dx

A: We will solve the problem

Q: For the DE y" + 9y = sin 3x : Use Variation of Parameters to find Yp

A: Given differential equation is, y''+9y=sin3x. In operator form can be written as, D2+9y=sin3x…

Q: xdx Q 1: Find the approximate value of I= using the trapezoidal rule with 6 equal subintervals. 1+ x…

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Q: cos(x) dx 1+ x2 a) Calculate using Simpson's 1/3 rule. b) Take n = 5 and calculate using the…

A: Solution:- The given integral  is  I=∫0π2cos(x)1+x2dx

Q: Q3/ Find ſ Vx * Sin (x³2 -1) dx=? (by substitution)

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Q: Q4) find 2 for : dx y = sin(x") + 2* +n

A: Use simple formula of derivative

Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. Given xy? =Sinlyz find dź/dk

A: We are given: x2+y2+z2=sinyz Differentiating both sides with respect to x, we have…

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

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

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Q: Q8// find the general solution (tan-'x + (cotx)y)dx + (lnsinx)dy = 0

A: The differential equation is given as (tan-1x+(cotx)y)dx+(ln sinx)dy=0 Compare it with Mdx+Ndy=0…

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

A: