Thursday

October 23, 2014

October 23, 2014

Posted by **Thomas** on Friday, June 24, 2011 at 2:26pm.

- Engineering Math -
**Count Iblis**, Friday, June 24, 2011 at 2:53pmcos(x) is the real part of exp(i x). You can then solve:

y' + 4 y = exp(i x)

and take the real part of the general solution (and then impose the boundary conditions). This is because the differential equation is linear and taking the ral part of both sides gives:

Re[y' + 4 y] = Re[exp(i x)] = cos(x)

And

Re[y' + 4 y] = Re(y)' + 4 Re(y)

The homogeneous part:

yh' + 4 yh = 0

as the solution:

yh = A exp(-4 x)

A solution to

y' + 4 y = exp(i x)

can be found by putting y = B exp(i x):

i B + 4 B = 1 ------>

B = 1/(i + 4) = (4-i)/(17)

So, we have:

y = (4/17 - i/17) exp(ix)

The real part of this is:

Re(y) = 4/17 cos(x)+ 1/17 sin(x)

The general solution is thus:

y = A exp(-4 x) +

4/17 cos(x)+ 1/17 sin(x)

You can then insert x = pi/3 in here and equate that to 1 to find A.

**Answer this Question**

**Related Questions**

Calculus grade 12 - solve for (<_ = less than or equal to / pie = pie sign...

Differential Equations - Solve the seperable differential equation for U. du/dt...

calculus-differential equation - Consider the differential equation: (du/dt)=-u^...

math - Can someone please help? Solve the differential equation dy/dx = 6xy ...

Engineering Maths - please help solve this differential equation: x^3+(y+1)^2 dy...

Math - Hi. please help me solve the ffg. differential equation: D^2y=3sinx-4y ...

Engineering Maths - Pleas help solve the ffg. differential equation: dy/dx-(1+1/...

Calculus - Solve the differential equation dy/dx=3x^2y^2 with the condition that...

math (differential equation) - show that y sub n=cos(ncos^-1(x)) satisfies the ...

Advance Math - Find solutions of the equation in the interval [0, 2pie} Cos(x+...