13. Find the general solution dy = sin x + y cot x: dx а. у %3D (х + с)(sec x + tan x) b. у %3 (x + с) sin x с. х*у — x tan y %3D с d. none of these

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Q: Solve the following initial value problem using the undetermined coefficients method: d'y dt2 + y =…

A: Given d2ydx2+y=8cos2x-4sinx with yπ2=-1,  y1π2=0

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Q: 5 By separation of variables, Solve the following PDES- ²4 = 4 24 dx² dt² 0 o u(e,t) = u(s, t) =6…

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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…

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Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

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Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

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Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: Solve the homogeneous DE. 3. (x – y sec?2 – x tan2) dx + x sec² 2 dy = 0 -

A: Given that: x-ysec2yx-xtanyxdx+xsec2yxdy=0

Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

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Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

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Q: Given that x(t) = c¡ cos wt + cz sin wt is the general solution of x" + w²x = 0 on the interval (-*,…

A: 10 Given solution of differential equation is x(t)=c1cos ωt+c2 sinωt of the differential equation…

Q: Solve the initial – value problem: xtan sec2. dy C :y(3) =0 2. eesc?ydx-Vr sinydy =0 :y (In's)= 3.

A: we can solve these question by variable separation and homogeneous function technique of solving…

Q: Consider the IVP: x" + x = 4e'; x(0) = 1, x'(0) = 3. Find the general solution. A x(1) = 2e+ sin21 –…

A: Some of the properties of the Laplace  L-11s-a=eatLeat=1s-aL-1ss2+a2=cosatL-1as2+a2=sinat

Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: The general solution of y"+ 16y cost is: Select one: a. y=C;cos(4f) + C;sin{at) =tcost 17 b.…

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Q: olve the following initial value problem using variation of parameters: y" + 4y = cos 3x y(0) = 0,…

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

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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

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Q: 2y cos x + sint x)dx = sin x dy vhen x= t/4 ; y=1

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Q: Find the general solution of (1+cosy)dx-x sin ydy = 0. (1) x – sin y – x cos y = C (2) x = C(1+ cos…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: Find the general solution of the DE: sin(z+y)dr + [2y+ sin(x + y)]dy = 0 O A. y- cos(z + y)-C O B. y…

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Q: Find the solution of the initial value problem dy y , y(1) = 5 + tan %3D %3D dx

A: Given initial value problem is dydx=yx+tanyx   y1=π2

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: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan…

A: This question is related to differential equation.

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.…

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Q: Find dy/dx a) y=(8x^2 - 9x + 11)^2

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: 4. Show that :| f(t) sin a(x – t)dt Y : solves the initial value problem dy +a²y = f(x), dx? dy 0…

A: Below is the answer

Q: determine (without solving the problem) an interval in which the solution of the given initial value…

A: Given: y'+tanty=sint, yπ=0 we know that solution of differential equationy'+pxy=qx is given by…

Q: Solve the following initial-value problem: V3 V1-y? dx - V1- x² dy=D0; y(0) = 2 O 2sin-1x+sin-ly=t/3…

A: Given: The differential equation 1-y2dx-1-x2dy=0 and initial condition y0=32, To Find: Solution of…

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

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Q: Find the general solution of the following IVP: (32²tany + 2) + (x³ sec?y – 1) = 0, y(0) = 0. %3D dz

A: Simplify the differential equation to exact form and integrate each terms.

Q: Find the general solution of the DE sec x dy = y dx. O In y = e^x +c O In y = sin x + c

A: Our Aim is to find the general solution of the differential equation given below:-sec (x) dy=y dx…

Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: 3y" – 6y' + 6y = e* sec x - Target Solution: 1 y = cie* cos x + cze* sin x + ; In(cos a)e" cos r +re…

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Q: 3y" – 6y' + 6y = e* sec x Target Solution: y = cief cos z + oze sin z+In(cos z)e" cos z +re sin z.

A: Given differential equation 3y''-6y'+6y=exsecx  We need to find the general solution of this given…

Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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

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

Q: (d) Using the method of characteristics, or otherwise, find the general solution to y-uy – xu, = 0,…

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Q: mü + ku = 0 subject to the initial conditions u = u(0) and ù = ü(0) is given by the equation u(0) -…

A: Here is the solution of the given second order differential equation.

Q: Solve the following initial value problem d'y dy + 4 + 4y = sin r, dr y(0) = 1, y'(0) = 0 %3D da?

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

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Q: Determine (without solving the problem) an interval in which the solution to the following initial…

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Q: III. EVALUATE THE FF. ITERA •rU/2 ptan y sec y 1. . x' cos ydxdy Jo . cosy sin2x dy dx xp, •3n /2 pn…

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