# Problem in solving system of equations using “Solve”

I have an equation in its normalized form as: $$\frac{v(x)}{V_{cc}}=C_1\cos qx+C_2\sin qx+1+ \frac{q^2}{1-q^2}.\frac{V_R} {V_{cc}}\sin (x+\phi)$$

Where $$q=\frac{1}{\omega\sqrt{LC}}$$ With the constants C1 and C2 equal to $$C_1= -\cos(q\pi)-q \pi \sin(q\pi)+(\frac{q}{1-q^2})\frac{V_R}{V_{cc}} \times\begin{bmatrix} q \cos(q\pi) \sin \phi +(1-2q^2) \sin(q\pi) \cos \phi \end{bmatrix}$$

$$C_2= -\sin(q\pi)+q \pi \cos(q\pi)+(\frac{q}{1-q^2})\frac{V_R}{V_{cc}} \times \begin{bmatrix} q \sin(q\pi) \sin \phi -(1-2q^2) \cos(q\pi) \cos \phi \end{bmatrix}$$

So I have set of three equations as follows

$$V_R= -\frac{1}{\pi} \int_{0}^{2\pi} v(x)\sin(x+\phi)dx$$

$$\begin{bmatrix}v(x)\end{bmatrix}_{x=2\pi}=0$$ and $$\begin{bmatrix}\frac{d v(x)}{d x}\end{bmatrix}_{x=2\pi}=0$$

I am trying to solve the above three equations for three unknown parameters $$\phi,q, V_R$$ whereas Vcc is a constant in my equations. The three unknown parameters are reported by the authors of the research article as

$$\phi = -41.614$$,$$q=1.607$$,$$V_R= 0.9253 \times V_{cc}$$

I am solving the above set of three equations using Solve in Wolfram Mathematica but I get the error message as Solve::nsmet: This system cannot be solved with the methods available to Solve. >>. The complete notebook code that I use in Mathematica to solve it is given below

Clear[x, y, A, q, b, c, ysol, ysolsimp, c1, c2]
A = \[Omega]^2*L*C
b = Vcc
c = VR
d = q^2/(1 - q^2)
phi = \[Minus]41.614
q = 1.607
Vcc = 1
VR = 0.9253*Vcc
eqn = Vcc + Vcc*c1*Cos[q*x] + Vcc*c2*Sin[q*x] + d*c*Sin[x + phi]
temp1 = D[eqn, x]
c1 = -Cos[q*Pi] -
q*Pi*Sin[q*Pi] + (d/q)*(VR/
Vcc)*(q*Cos[q*Pi]* Sin[phi] + (1 - 2 q^2)*Sin[q*Pi]*Cos[phi])
c2 = -Sin[q*Pi] -
q*Pi*Cos[q*Pi] + (d/q)*(VR/
Vcc)*(q*Sin[q*Pi]* Sin[phi] - (1 - 2 q^2)*Cos[q*Pi]*Cos[phi])
temp2 = -(1/\[Pi])*\!$$\*SubsuperscriptBox[\(\[Integral]$$, $$0$$, $$2 \[Pi]$$]$$eqn* Sin[x + phi] \[DifferentialD]x$$\)
eqn1 = temp1 == c
eqn2 = eqn *b == 0 /. x -> 2*\[Pi]
eqn3 = temp1 == 0 /. x -> 2*\[Pi]
Solve[{eqn1, eqn2, eqn3}, {phi, VR, q}]

Solve::nsmet:This system cannot be solved with the methods available to Solve. >>


The complete Wolfram Mathematica Notebook is also attached to this post. Kindly help me to debug the error. How can I get the same answer as that of the research article? Thanking you.

• wolframcloud.com/obj/ebad13d0-9543-48da-9477-1140be4a482d – Liyaqat Apr 1 at 7:44
• I think you can make the question simpler by just listings the equations and indicating which variables you are trying to solve for. It is hard to read of all this just to find this information out. – Nasser Apr 1 at 7:44
• @Nasser Thank you for your valuable reply. I have edited the post and tried to make it simpler for a better understanding. Looking forward for your valuable suggestions. Thank you – Liyaqat Apr 1 at 11:02
• Please edit your code by converting to Raw InputForm (menu: Cell | Convert To | Raw InputForm) prior to copy and paste here. – Bob Hanlon Apr 1 at 14:25
• @Bob Hanlon Thank you for your comment. I edited the code after following the steps mentioned in your comment. Looking forward to your valuable feedback. Thank you – Liyaqat Apr 1 at 15:00