18. What will be the value (if any) of the particular solution of the problem u (1+ cost)u=1+ cos t, u(0) long period of time? 3 over a (a) (b) u=1+2e-( sint) (c) 4.4). (d) u=1+e-(t-sint) (e) None of the above 19. Determine the degree of homogeneity of the following multi-variabeuction f(z, u) = tan u? (a) 1 (b) 2 (c) 0 (d) Non-Homogeneous (e) None of the above.

Q: 15. What is the general solution of the exact differential equation (x + siny – cosy)dx + x(siny +…

A:

Q: 43. Given that y = sin x is an explicit solution of the first- dy order differential equation VI -…

A:

Q: 7. What is M(x,y) for the following differential equation: x(1 – sin y)y' = (cos x – cos y – y)

A:

Q: (30. y4) +y" = 0; 1, x, cos x, sin x, (-, 0)

A:

Q: dx 5x cos(3t) dt with x(0) = -4.

A:

Q: Find the particular solution of the differential equation = 10y sin(x) using the given boundary…

A: To find the particular solution of the given differential equations

Q: Given the differential equation 2 y" + 18y = 6 tan(3x) Determine the value of u2. AH2 "3 =" 9*…

A:

Q: B. Solve for the differential equation of the following families of curves: (1) Family of parabolas…

A:

Q: 04- Determine the general solution of the following differential equat dy tan x. +у %3D sec х dx

A:

Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

Q: Obtain the differential equation of the family of circles of fixed radius r with center on the…

A: We have to obtain the differential equation of the family of circles of fixed radius r with center…

Q: ду 9. The differential equation (3ycos.x+4xe" +2x'e" dx+3(sin x+1)dy 0 is exact because ON 10. The…

A:

Q: Particular Integral for the differential equation ( D +D+4)y =sin2x is given by cos2x a. O b. cos2x…

A: By the using rule of particular Integral we can find integral

Q: (a) To determine To compute: The initial value problem + 4x = sin 4t with initial conditions x (0) =…

A: The given differential equation is: d2xdt2+4x=sin4t, a) for x(0)=0, x'(0)=v0>0 we have to find…

Q: Find the particular solution to the differential equation: dy dx 3x2 cos? y. Solution passes through…

A:

Q: sin x sin y dx + cos x cos y dy = 0 %3D

A:

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: First I have made the differential equation into variable seperable form and then solved them.

Q: Find the solution to the differential equation that satisfies the given condition. I am having…

A: Given differential equation can be written as Integrating both sides , we get

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

A: To find- Show that an implicit solution of 2x sin2y dx - x2 + 17 cosy dy = 0 is given by lnx2 + 17 +…

Q: Solve the initial value problem: cos z – 3x?y – 2æ) dx + (2y sin x – x° + In y) dy = 0; y (0) - -- -…

A:

Q: 5. In the differential equation (1+3xsin ykdx-x cos ydy = 0, we let the substitution %3D

A: Follow the procedure given below.

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: 7. What is M(xy) for the following differential equation: x(1 – sin y)y' = (cos x – cos y – y) x- x…

A:

Q: For which value(s) of r is y = x" In(x) a solution of the differential y (3 In(x) + In(x)

A:

Q: 2. Consider a spring-mass system with an external force 36(t – 4) + sin(t), which is described by +…

A: Spring mass system described by the DE  y''+2y'+y=3δ(t-4)+sint clearly at t=0, y=0 and y'=0 Taking…

Q: 5. With the substitution cosy == differential equations sin y dy – cosy(1 – x cosy)dx=0 reduced to a…

A: Substitute  cosy=1tNow differentiate it with respect to t,-sinydy=-1t2dtsinydy=1t2dt

Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: 1. Find the differential equation of the family of circles of radius r whose centre lies on the…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

Q: 4) Let y(x) be the solution of the initial -value problem y' = cos(x + y), y(0) = 0. Use Euler's…

A: To find the solution of initial value problem.

Q: For x € 0,, What is the particular solution of the differential equation (y + ysinx)y' = /cos?x –…

A:

Q: 2. Find the correct form for the particular solution but DO NOT determine the coefficients. (Hint:…

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Q: (3tan x – 2cos y ) sec 2 xdx + tan x sin ydy = 0 %3D

A:

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: NUTES -3x PG. 8 Problem q: y" =94iyse",y2s e3*

A:

Q: 22/ for the differential equation ģ =X+y if ylo)=1 s ind y (ood) by Using Euller modibied method…

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: y'+ytan(x)=cos^2(x) ,      y(0)=-1

A:

Q: Apply Euler's method to approximate the solution of the initial value problem y' = 2 cos(2x) cos(y),…

A: We have to find the value of y(2) using Euler's method for approximation.

Q: Verify that the indicated function y = y(x) is an explicit solution of the given first-order…

A:

Q: In the following problems, obtain the differential equations of the given families of curves whose…

A: Parabolas with vertex on the y-axis, with axis parallel to the x-axis, and with distance from the…

Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

Q: y" + 2y' + y = −e* [(− x² + 4x+3)cos x + (− x² + 4x + 3)sin x]

A: As per the question we are given a second order linear non-homogeneous differential equation. And we…

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.