5. Show that the following differential equations are exact. (b) (2ye* +cos x)dy –(e¯*y² – y sin x)dx =0

Q: 2. Solve the following differential equation in two ways: once using separation of variables, and…

A: Here we have to use variable separable method and reverse product rule to solve the differential…

Q: Find the general solution to the following differential equation. y" – 3y = 7 cos(3x) – (x+ 1)…

A: The general solution will be the sum of the complementary solution and particular solution.   The…

Q: 4) Find the general solution to the following differential equation y" + y = tan(t)

A: Find first homogeneous solution y''+y=0. The roots of auxiliary equation m2+1 is  m=±i Then…

Q: Find the particular solutions of the given differential equation dy dz 2 cos a sin a given y = 1…

A: 1. Sin(2A)=2sin(A)cos(A). 2. Sin²A+Cos²A=1.

Q: dy In(1 – x) + dx y = cos x, y(0) = 0 х-1

A: The differential equation is given as ln(1-x)dydx+yx-1=cos x It can be rewritten as…

Q: Find the particular solution to the following separable differential equation. dy x? and y(3) = 2 dx…

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: Find the general solution for the following differential equation: y" – 3 y' + 2 y = cos e-*

A: to find the general solution , consider the  equation y''-3y'+2y=0  the auxiliary equation is…

Q: 2. Find the general solution to the following differential equation: (2x – 8x) sin(In y)y' = x + 3.…

A:

Q: Find the general solution of the following differential equations: (y² + 3)dx – () ydy = 0 - (cos(x…

A:

Q: (a) Evaluate the general solution for the following differential equation. dy (Inx) y = 0 dx

A:

Q: I. FIND THE GENERAL SOLUTION OF THE FOLLOWING DIFFERENTIAL EQUATIONS: tan xdy (x tan x+ In y)dx 0 =…

A:

Q: An appropriate integrating factor µ(x) for the following differential equation (2y² + 3x)x+ 2xydy=0…

A:

Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 17y…

A:

Q: 8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0…

A: Phase portrait of x''+10x'+24x=0 Phase portrait of x''+2x=0

Q: 2. Solve the following Exact Differential Equation with boundary value y(1) = 1 (x + y)²dx + (2xy +…

A:

Q: Obtain the particular solution for the following differential equation if y(7) = 1 (3x² + ycosx)dx +…

A:

Q: ive a general solution to the following differential equation: ya) – 2y" +y = x cos r

A:

Q: 8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0…

A: Differential equations as it's phase portraits given below

Q: 1) Find the general solution to the following differential equation. dy +y (cotx) = 5e* dx %3D

A:

Q: 25.Find the general solution of the differential equation dPy dy 3 +2y 2 sin 28-4 cos 20 %3D dez de

A: We use the method of variation of parameters to solve the given differential equation.

Q: y' + }xy = sin(x 4e¤2 y3 1

A:

Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 16y…

A:

Q: 2. Solve the differential equation as follows: (e4y cos x + 8x³ y³)dx + (4e*y sin x + 6x*y² + 8y)dy…

A: the equation is of the type Mdx+Ndy=0 where M = e4ycosx+8x3y3 and N = 4e4ysinx+6x4y2+8y  calculate…

Q: 3. Solve the Bernoulli's Differential Equations dy x = y + y°cosx dx

A:

Q: Obtain the particular solution for the following differential equation if y(n) = 1 (3x2 + ycosx)dx +…

A: Detail solution written below

Q: 10. Verify that the given differential equation is exact; then solve it. (8 cos x + In y)dx + dy = 0

A:

Q: 1. Evaluate the solution for the following differential equation et y" – 2y' + y = x2

A: We solved above differential equation by variation of parameter.

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

A:

Q: 1) Find the general solution to the following differential equation, (2xy? – ysin(x) + 2x + 1)dx +…

A: The given differential equation is  (2xy2 - ysinx +2x +1)dx + (2x2y + cosx +1y)dy =0

Q: (5) Find the solution of the following separable differential equation: dy -x(y + 2)², y(0) = 2. dx

A:

Q: -. (ex. + Iny + 2) dx + +In+siny) dy = 0 sin y)

A: To solve the given differential equation

Q: 7) ( x² + 6y? ) dx - 4xy dy = 0 y(1) = 1

A:

Q: Find the general solution for the following differential equation: y'' -3y' +2y =cos⁡〖e^(-x) 〗

A:

Q: Obtain the particular solution for the following differential equation if y(n) = 1 (3x? + ycosx)dx +…

A:

Q: Find the solution of the following Differential Equations 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy 7)…

A:

Q: Solve the seperable differential equation for. dy 1+1. -; r>0 rys dr Use the following initial…

A:

Q: Find the solution of the following Differential Equations .by Exact sin(ß y)dx =-ßcos(ß y)dy

A: Let us discuss what is exact differential equation. An ordinary differential equation of the form…

Q: Find the general solution of the following differential equation:  ( 2xy + sin2x - tany ) dx + ( x2…

A:

Q: 4. Solve the following Second Order Differential Equation dy dy + 6- d.x 9. + 5y = 0 dx?

A: Given : 9d2ydx2+6dydx+5y =0

Q: Show that the following differential equation is an exact equation. (2x+xy-1)dx+(x'y+3)dy = 0,…

A:

Q: 1) Find the general solution to the following differential equation. dy + y (cotx) = 5e* dx

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: What are the associated roots forR (x) in the differential equationy''- y = R(x) where R(x) = 4cosx?…

A: Given differential equation:- y"-y = R(x) Where R(x) = 4 cosx

Q: 5.Given that xsinx is a particular integral of the differential equation y" +y = cosx, the value of…

A: Given DE y"+y=cosx Particular integral y=λxsinx

Q: 2. Obtain the general solution of the following first order differential equations. sin x sin y dy +…

A:

Q: 3) ( y³ + × )V = 1 x (2) = 1

A: In the given problem initial conditions was wrong it should be y(2) =1 instead of x(2) =1, since 'y'…

Q: dy + 6ycos3x = cos3x dx

A:

Q: 4. 2ydx + (x x³y³) dy = 0

A: Here we have to solve the given differential equation