Derive the working differential equation for the given circuit, R i(t) → VR V(t) O + iR= E (t) * + iR + L = E (t) %3D dt * + iR + L = E (t) O iR + L = E (t)
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A: Correct ans is option = D Please find attachment for the details solution
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- Convert the equation into a first-order linear differential equation system with an appropriate transformation of variables.Consider a disease where immunity is lost. On average, aftern days, a recovered person becomes susceptible again. Adjust the equationsfor ds/dt , di/dt, and dr/dt in the SIR model to account for this.Solve the second-order differential equation [1, 1/x, 4(x^2-25/x^2)]y=0 by applying the variable transformation x=sqrt(t) and convert it into a Bessel's differential equation
- (du/dt)^3 – (du/dt)^2 – 2u = 0Is the differential equation in the image autonomous? Does the differential equation have any equilibrium solutions?Consider the autonomous differential equation dx/dt=-7(x+1)(3-x)(x-5)^2 Find the equilibria, draw a phase line for the differential equation, and then classify the equilibria. Finally, sketch representative solutions to the differential equation based on the phase line.
- solve the exact differential equation: (6x2 +4xy + y2)dx + (2x2 + 2xy -3y2)dy =0 2x3+2x?y+xy2-y³=c .A 3x2+2x3y+xy2+y°=c_BO 2x³+2x?y+xy2-2x²y-y²x-y²%=c_co 2x³+2x3y+xy²+2x²y+y²x-y³=c .D O Bb Bb W 直 。 图Write the equation „dr te +x dt dr in the form of +p(t)x=q(t). Then identify p(t) and q(t). dt Select one: O a. da - dt P() =-! 9(t)=e 1 t O b. dx dt p(t)=- 1 q(t)=e O c. da_ x dt t p(t)=- q(t)=ei +