What is the general solution of the differential equation? : # (d^2y)/(dx^2) + dy/dx - 2y = -6sin2x-18cos2x#
# y(x) = -e^(-2x) + 3cos(2x)#
We have:
Complementary Function
The homogeneous equation associated with [A] is
And it's associated Auxiliary equation is:
Thus the solution of the homogeneous equation is:
Particular Solution
With this particular equation [A], a probably solution is of the form:
Solving simultaneously we get:
And so we form the Particular solution:
General Solution
Which then leads to the GS of [A}
Initial Conditions
We are given the initial conditions:
Solving these two new equations simultaneously we get:
leading to the specific solution:
By signing up, you agree to our Terms of Service and Privacy Policy
The general solution to the given differential equation is:
[ y(x) = c_1 e^x + c_2 e^{-2x} + 3 \sin(2x) - 6 \cos(2x) ]
Where ( c_1 ) and ( c_2 ) are arbitrary constants.
By signing up, you agree to our Terms of Service and Privacy Policy
The general solution of the given differential equation is:
[ y(x) = C_1e^{2x} + C_2e^{-x} - 3\sin(2x) - 3\cos(2x) ]
Where ( C_1 ) and ( C_2 ) are arbitrary constants.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- What is a solution to the differential equation #dy/dx=x/(x+y)#?
- What is the arc length of #f(x)=2/x^4-1/x^6# on #x in [3,6]#?
- What is a solution to the differential equation #(dy/dx) - y - e^(3x) = 0#?
- How do you find the volume of the bounded region if #y = sinx#, #y = 0# from #x = pi/4#, #x = 3pi/4#, revolved around the y-axis?
- How do you use differentials to estimate the maximum error in calculating the surface area of the box if the dimensions of a closed rectangular box are measured as 60 centimeters, 80 centimeters, and 90 centimeters, respectively, with the error in each measurement at most .2 centimeters?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7