Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" + xy' + y = 0, 0 < x < 0. Find the general solution of 2?y" + xy' + y = g3/2

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

A:

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

A:

Q: Find general Solution of DE =0 on Co, mo). AISO how that xJú (x)-VJ,(x) + x Cn)

A:

Q: Suppose that x1(t) = et and x2(t) = e-t are two solutions of a homogeneous linear differential…

A: The answer is found in step-2

Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

A:

Q: . Use Regula-Falsi method to find solutions of x = cos x which is accurate to within 10-8 . Take x,…

A:

Q: 9. Use the Secant method to find an approximation to the solution of sin(x) - e-* = 0 in [0, 1]…

A:

Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: x³y"+xy'+4y = cos (2 In x)

A:

Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

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

Q: Given that x(t) = c1 cos omega t + c2 sin omega t is the general solution of x'' + omega2 x=0 on the…

A:

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

A:

Q: Solve the given differential euation: dr/dθ+rtanθ=10cosθ. 1.r=(10θ+C)tanθ 2.r=(10θ+C)cosθ…

A: In this question we have to solve the given differential equation.

Q: Show that y1 = sin x² and y2 = cos x² are linearly in- dependent functions, but that their Wronskian…

A:

Q: 5. Find all solutions of 2 cos x- -cos x-1 0 if 0sxs2n.

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

Q: If y, = u1 (t) cos(5t) + u2(t) sin(5t) is a particular solution of the differential equation y" +…

A:

Q: 5. Find the general solution to the DE using the method of Undetermined Coetficients: y" + 9y = 2…

A:

Q: iFind the general solution of the equation sin4x 19. Find the general solution of the equation cos2x…

A:

Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

Q: If the auxiliary roots of a certain homogeneous linear differential equation are 2 + 31, #3i, +31,…

A:

Q: 2. Evaluate the integral (cos (3r)sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

A:

Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

A:

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: Calculation shown in the solution is correct , i am providing you the  answer for each boxes…

Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

A:

Q: Without solving for the undetermined coefficients, the correct form of a particular solution of the…

A:

Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: It can be shown that y, = 2 and y, = cos²(9x) + sin²(9x) are solutions to the differential equation…

A:

Q: '+y- y²(cos 2x– sin 2x) = 0

A:

Q: sin(ax)y = -a cos(a.x)y + a

A: Given that  The differential equation  To find the general solution

Q: Find the general solution to the DE using the method of Undetermined Coefficients: y" + 9y = 2…

A:

Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

Q: Show that an implicit solution of 2x sin2(y) dx - (x2 + 19) cos(y) dy = 0 is given by In(x² + 19) +…

A:

Q: Verify by substitution that the family of functions y = -(x) sin(-3x) + cx is a solution of the…

A:

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

A:

Q: Use Euler method to estimate the solution of 1 sin 5x - 5e cos 5.x, dx with initial condition v(0)=0…

A:

Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: Suppose y₁ = sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential…

A: To find the differential equation :-

Q: Solve the first order differential equation to find the particular solution. (cos x) + y sin x = 2x…

A: To solve the given differential equation.

Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

A:

Q: A particular solution for y +2y +y=1-cosX

A:

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

A:

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

A:

Q: The solution to the differential equation -y x cos(3x) - is: Select one: cos(3x) + cx2 O 3x² sin(3x)…

A:

Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

A:

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 =…