Question

solve the differential equation

1) ? ′′ − 2? ′ + 10? = ? −?

2) ? ′′ + 5? ′ + 4? = sin(3?)

3) ? ′′ + 9? = 2 sin(?) + cos(?)

Answer #1

Solve the given differential equation by undetermined
coefficients.
y'' + 2y' + y = 2 cos x − 2x sin x

Solve (3D^2+D-14)y=8e^2x +Cos 5x.
Solve the differential equation by variation of
parameter
Solve the differential equation by variation of
parameter (3D^2+D-14)y=8e^2x+Cos 5x

Determine whether the given differential equation is exact. If
it is exact, solve it. (If it is not exact, enter NOT.)
(tan(x) − sin(x) sin(y)) dx + cos(x) cos(y) dy = 0

solve the following differential equation
4a) ? ′′ + 2? ′ + ? = 3? + 8
5a) ? ′′ + 4? ′ = 5

Solve the given equation
2 cos^2 theta+sin theta =1
cos theta cos 20 + sin theta sin 20= 1/2

Solve the following differential equations
1. cos(t)y' - sin(t)y = t^2
2. y' - 2ty = t
Solve the ODE
3. ty' - y = t^3 e^(3t), for t > 0
Compare the number of solutions of the following three initial
value problems for the previous ODE
4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0
Solve the IVP, and find the interval of validity of the
solution
5. y' + (cot x)y = 5e^(cos x),...

Find an appropriate integrating factor that will convert the
given not exact differential equation cos x d x + ( 1 + 2 y ) sin
x d y = 0 into an exact one. Then solve the new exact
differential equation.

Solve the following Differential equations
a) x sin y dx + (x^2 + 1) cos y dy = 0

Partial differential equations
Solve using the method of characteristics
ut +1/2 ux + 3/2 vx = 0 , u(x,0) =cos(2x)
vt + 3/2 ux + 1/2 vx = 0 , v(x,0) = sin(2x)

1. Solve sin(x)= √2/2 over the interval [0,2π).
2. Solve 4cos(x)+1=3 over the interval [0,2π).
3. Solve cos^2(x)+6=7 over the interval [0,2π).
4. How many solutions are there for the equation
4cos(x)+5=6 over the interval [0,2π).

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