4. Find the particular solution of the differential equation (10x + 6x siny)dx + Vx? +1(1+6ysiny+10y)dy = 0 with x = 0, y = 0. Using the resulting particular solution, find x? if (a) y = 1 and (b) y = n/2.

Q: Determine the general solution of the given differential equation. -t y""+y" + y + y = et +9t NOTE:…

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Q: 10. Find the general solution of the first-order linear differential equation. dy dr y = el 10x

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Q: Solve for the general solution of the below differential equation. y" + 3y' + 2y = cos x

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Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: Given that        y''+y'2+4=0‐‐‐‐1        we have to solve this using the substitution        u=y'

Q: 2xydx = (x2 + y²)dy ;y(0) = -1 Ans: y(y + 1) = x²

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Q: 1. Find the general solution of the differential equation (1+ 9x²) cos y dy – 3(1+ sin y) dr = 0.

A: we have to solve this by separation of variable

Q: If a nonhomogeneous linear differential equation has g (a) = sin 5a, what is the form of its…

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Q: Solve the differential equation y" + y' +y = sin(2t) subjected to the conditions y(0) = -2/13 and…

A: solving by Laplace transformationgiveny''+y'+y=sin2t and y(0)=-213 ,y'(0)=713taking laplace on both…

Q: 10. Find the general solution to a sixth-order linear homogeneous differential equation for y(x)…

A: We first write the possible roots of the auxiliary roots  of auxiliary equation of  the sixth order…

Q: # 2.) Given the differential equation, y'=4cosx-3y, y(0)=1, a.) Use Euler's Improved Method to…

A: Given the differential equation, y'=4cosx-3y With the initial condition y(0)=1 Here,…

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

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Q: 2. The differential equation (4x'y -6xy-2x-3dx + (2x*y – 2.x' kdy = 0 is exact because ƏM ON dy

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Q: 1. Consider the differential equation: dy = = 2y - cos (3t) dt a. Find the homogeneous and…

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Q: 1. Determine whether or not y = C, cos(4t) + C2 sin(4t) is a solution to the differential equation…

A: Given differential equation  is y''+4y=0It is asked  to check if the solution  is,y=C1  cos  4t+C2…

Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: ( 3x - y +1) dx - ( 9x - 3y – 3 ) dy = 0

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Q: 4. Find the general solution of the differential equation using the method of undetermined…

A: Let's find.

Q: 1) Use the Method of Undetermined Coefficients to find the General Solution to the Differential…

A: Given : Differential  equation is            y'' - 4y' - 12y = 2sin(t) To find: Find the general…

Q: Determine whether y 3 sin 2x + e-a is a solution to the differential equation y" + 4y = 5e

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Q: 1. A solution for the differential equation is y = e"* A, sin (vx) + A2 cos (vx) , where m and n are…

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Q: In this problem, x = c, cos t + c, sin t is a two-parameter family of solutions of the second-order…

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Q: Find the general solution of the first-order linear differential equation for x > 0. (Use C for any…

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Q: Find a particular solution y, of the differential equation: y" + 9y = 2 cos 3x + 3 sin 3x

A: Explanation of the answer is as follows

Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

A: Let us consider a differential equation of the form Mdx+Ndy=0 To equation is exact if ∂M∂y=∂N∂x then…

Q: B/ Find solution for the homogenous differential equation below: dy x² +y² dx 2хy

A: Given differential equation is dydx = x2+y22xy

Q: B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy…

A: Let's find.

Q: 2. Solve the differential equation dy + xy = xy "Bernoulli" dx with y(0) = 1/2.

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Q: Find the general solution of the first-order differential equation                        x dx + ( y…

A: Consider the following differential equation: xdx+y+eyx2+1dy=0y+eyx2+1dy=-xdxy+eydy=-xx2+1dx…

Q: 16. What is the particular solution of the linear differential equation y' +y = sec e", whose…

A: The solution is given as

Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: 3. Find the general solution of the first order linear differential equation and use it to determine…

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Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: Consider the ordinary differential equation y'' + 4y'+2y=0 such that a solution is of the form y and…

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Q: 5.- Use the method of undetermined coefficients to find a particular solution, Y, , for the given…

A: Take up in perfect form and put on the given differential equation

Q: x(1+ y³)dy + ydx = 0 ;y(1) = 1 Ans: In(xy)3 + y3 = 1

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Q: 2) find the complete solution of the differential equation x dy +Jx²-y*dx = ydt

A: given xdy+x2-y2dx=ydxxdy=(y-x2-y2)dxdydx=(y-x2-y2x)put…

Q: For the differential equation y' + 4y = 0, a general solution is of the form y = C, sin 2x + C2 cos…

A: Given initial value  problem y"+4y=0    , y(0)=-2 , y'(0)=-10 y=c1 sin2x  +c2 cos2x

Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: b) Euler's method is used to solve a first-order differential equation dy dx from x = 0 to x = 4

A: We need to write Euler's method to solve the differential equation: dydx=f(y,x), from x=0 to x=4.

Q: dy (e2y – y)cos(x)- e' sin(2x), dx y(0) = 0

A: on solving this we get the

Q: dy 2y2 + x²e=(÷)² dx 2xy

A: dydx=2y2+x2e-yx22xy----(i)Let y = xudydx=xdydx+uPut the value of y and dydx in equation (i) we get…

Q: A. Obtain the differential equation of the given solution by eliminating the arbitrary constant(s):…

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Q: The y(1) value of the y'= x + y differential equation that satisfies the condition y0)=1 by taking…

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Q: 5. The differential equation (3r*e" - 2xktx+(r°e' -sin y}dy = 0 is exact because ƏN ƏM ôx

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Q: Write down the form of the general solution y = y. + y, of the given differential equation in the…

A: Consider y=emx be the solution of the homogeneous part. The auxiliary equation is m2+w2=0. Simplify…

Q: Determine the solution x(t) of the ordinary differential equations with initial values a. x"(t) -…

A: The Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that…

Q: The solution of the following separable differential equation x²y-y ア=リーン y' with y(3) = -1 is y+1…

A: Given,          y'=x2y-yy+1 with y3=-1

Q: 2. Find all values of r for which y = e™ is a solution of the second order differential equation y"…

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