Solve the given initial-value problem, y" +49y = 0, y(0) = 6, y(0) = -3 3 v(x) = 6 cos (71) - 2 sin(71)

Q: Solve y"-4y + 5y = mxe* sin(x)+(m+3) cos(x) by the method of undetermined coefficients.

A: From the given nonhomogeneous equation, solving the homogeneous equation:

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

A:

Q: Solve sin(x) +7 sin(x) cos(2x) = 0 for x E (0, 5). Give your answer in radians correct to 3 decimal…

A: The given equation is sin(x)+7sin(x) cos(2x)=0 and the range for x is (0, π/2).

Q: Solve D.E using bernouliis equation os(y)·y' + sin(y) =x

A:

Q: Solve the ode y''-6y´+13y=0;  y=exp(3x)  cos(x)

A:

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

A:

Q: Solve: y" + 2y' + 2y = 2 sin(x) +3 cos(2x)

A:

Q: 4 sin(x) cos(z) + 2 sin(z) – 2cos(z) – 1 = 0

A:

Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: 21) Find the number of compositions M needed so that the error of the integral 2.2 In(x + 2) dx is…

A: Simpson's rule can be used to approximate the value of the integration using numerical integration.…

Q: Find the solution of with y(0) 3 and y' (0) = 8. y = y" + 3y = 108 sin(3t) + 36 cos(3t)

A: see below the answer and explanation

Q: Use the method of undetermined coefficients to solve y" – 2y' + y = 5 cos(2x) + 10 sin(2x)

A: Solve the differential equation y"-2y'+y=5cos2x+10sin2x using the undetermined coefficients .

Q: Find the root

A:

Q: Find the solution of y" + 4y = 160 sin(4t) + 224 cos(4t) with y(0) = 3 and y' (0) = 2. y =

A:

Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: f (t) =-e" sin (21 +7)

A:

Q: Find the solution of with y(0) = 9 and y'(0) = 7. Y y" + 3y = 126 sin(3t) + 162 cos(3t)

A:

Q: (xy cos.xy +sin xy)dx +(x² cos.xy +e' )dy=0.

A: We have to solve given problem:

Q: Q2: Find General Solution (YGS)to the equation (Yª-1) Y=COS(2x)

A: From the given information. The given differential equation is as follows.

Q: Solve the ODE y" + y = et cos(2t) cos(2t) y(0) = 2, y'(0) = 1

A:

Q: Find a particular equation for: y(4) + 8y''' + 32y'' + 64y' + 39y = e-2x[(4 - 15x) cos 3x - (4 +…

A: The given equation can be written as, y4+8y3+32y2+64y1+39y=e-2x4-15xcos3x-4+15xsin3x it is also can…

Q: Determine the solution by the method of undetermined coefficients. y''+4=cos(2x)

A: