1. Solve the following ODE using separable variable method: dy +(x+ 2)y' = 0. dx а) dy (x +4) b) = 0 dx x(y +4) c) cot 2x dy +sin 2y dx =0

Q: Find the general solution. 1. (2xy-3x2)dx + (x2+2y)dy=0

A: According to company rule we can answer only first question and rest can be reposted

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

A:

Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

A:

Q: -3 Evaluate the triple integral ²³ sin(y²) dz dx dy.

A:

Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2…

A:

Q: 15. Solve d²y +3 y + 2y = 3 sin x, given that when x 0, y =-0-9 Wor, OFer dx? dx dy =-0-7. dx and…

A:

Q: Given: a = 0 – sin 0; y= 1- cos 0 d'y Find: dz2 O d'y 1 dz2 (1-cos 0) d'y 1 %3D dz2 (1-cos 0) O dy 1…

A:

Q: 5. Use Newton-Raphson method to find solutions accurate to within 10-2 for x - cos x = 0 on [0,…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 1. Given the DE as x(1 – siny)dy = (cosx – cosy – y)dx a) Prove if the given DE is exact or…

A: Given differential equation: x( 1- siny) dy=( cos x-cosy-y) dx

Q: 2. Evaluate a. [x'(2x° +5)' dx b. dx V1-7x c. [cos 3xsin 3xdr d. sin* 6x cos 6xdx e. [t* cos(2r'…

A:

Q: Solve dN dt = (1¹ 1+ cos(2nt) N where t ≤0 and N(0) = No.

A:

Q: Consider the following first-order ODE where y is the dependent variable and x is the independent…

A:

Q: If the RHS (Right Hand Side-the source) function of a second-order differen tial equation with a…

A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: Find the general solution of 2ydx + (x – sin Jy)dy = 0.

A:

Q: Question 2 Find the differential dy: y= sin O dy E In a + sin( rVE dr Cos ( xY O (E) None of these…

A:

Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: 1. Solve the following ODE using separable variable method: dy а) +(x+2)y =0. dx dy (x +4) b) =0 dx…

A:

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

A:

Q: 1. 5. Find the value of the line integral. (x - y) dx- 2.xy dy C:r(t)=2 cos ti + sin ti

A:

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

A:

Q: Find the general solution of the given nonhomogeneous equation. x^2y''+xy'+y=sec(Inx) ;…

A:

Q: () = 2 + Solve the initial value problem : f'(x) = cosx + sec?x, %3D

A: As you post multiple questions we only solve first question only.

Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: 2 Consider solving dx using a suitable trigonometric substitution. After performing substitution…

A:

Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: Find the solution of the following IVP. * (yexy) dx + (xexy + sin(y))dy = 0, exy + cosy - 1 = 0 O…

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

Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

A:

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

A:

Q: 1. [* sin'x cos xdx parctan3/2 3secx 2. y dy dx 3. T y xpáp X 4. [S yz dx dy dz ea/4 2cose prsine 5.…

A:

Q: 13. Find the differential dy for each of the following. a) y = cos 2x- sin 3x b) y = x2 – V36 – x² |…

A:

Q: (b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

A:

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: 1. Solve the following ODE using separable variable method: dy +(x+2)y³ =0. dx а)

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

Q: The linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is:

A:

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

A:

Q: 1. -ay + A sin dy 2 = Br, dt

A:

Q: 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

A:

Q: 9. Find the general solution: (3x²y – sin y)dx + x(x² – cos y)dy = 0

A:

Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

A:

Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute…

A:

Q: 3) I Cos dydx Ins Iny 4) S S e** dxdy X 1 0

A: 3)  Given:      ∫π2π∫0x21xcosyxdydx       =∫π2π∫0x21xcosyxdydx

Q: Solve the following dy 1. xy dx = 2y2 - x2 %3D | dy 2. x2 dx xy = (x² + y²) tan-() (x + y2) tan-1 dy…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1.) 201 4sin (x) cos (x) dx dy 0 y² + 1 [¹ylnª (y² + 1)

A:

Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

A:

Q: A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its…

A: given velocity of the particle at time 't' v=3t2i+2cos4tj+t2k initial position x(0)=2i

Q: 10. Solve the following ODES by separating variables (a) dx Cos 5t where x(0) = 1 dt x2 (Ъ) dy e2y+t…

A: Given: (a) dxdt=cos5tx2 where x0=1  (b) dydt=e2y+t To determine: The solution of given ODEs by…