An electric circuit has a constant electromotive force E = 40v, a resistor of      R = 10Ω and an inductance L =0.2 henry (H), with initial current I =0 at t =0 and basic differential equation is:  L dI /dt +RI = E. Determine the current at any time t.

Q: Consider the differential equation (DE) y" +t(y')² = 0. a) Its i) order is ii) degree is b)…

A: Given differential equation,     y"+ t(y')2 =0 We have to find  Degree Order  And no of conditions…

Q: - ysin)dn t x sint

A: See the details solution in below

Q: Consider the differential equation (DE) x' +3, + y = sinh x + 2 da2 a) Its i) order is ii) degree is…

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Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

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Q: Given, ( +) dx + ( y4 Aæ+1) dy = 0 is an exact differential equation. %3D Determine the value of A.

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Q: The charge g= g(t) in the capacitor in an RLC circuit satisfies the differential equation da 800 dt…

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Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

Q: Is (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Exact differential equation- A differential equation of the type Mdx+Ndy=0 is said to be exact if,…

Q: dy +ky = a sin bx dx %3D Show that the solution of the differential equation is given by: 2 +b²+ab K…

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Q: The equation k(dQI dt) + Q(t) = I(t) has been used to describe the response Pof streamflow to a…

A: We have to solve the differential equation.

Q: Suppose the lateral displacement of the center of a bridge may be modeled as a spring-and-mass…

A: Please see the next step for solution.

Q: %3D

A: Find the second derivative and substitute in the given differential equation and solve for r.

Q: The value of the constant a such that the given differential equation is exact ) 1 1 dx + 1 dy = 0…

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Q: A 30-V emf is connected in series to an inductance of 0.1 henry and a resistance of 50 Q. Initially,…

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Q: Given the non-homogeneous second order differential equation:: y" – 4y = sin(5æ) the general…

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Q: In a spring mass system the displacement, x meters, of an object from its equilibrium position with…

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Q: A block of mass= 1 is sitting on a table and is attached to a spring of strength k=5 so that it can…

A: The differential equation governing the spring-mass system is  m dx2dt2+ b dxdt+ kx = F(t) where,…

Q: 3. State the order of homogeneity and solve the differential equation as a homogeneous equation. х…

A: The objective is to state the order of homogeneity and solve the differential equation as a…

Q: Suppose that the heat conduction in a rod of length Lis described by the equation ku- hu, 0 0, at…

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Q: Consider the forced but undamped harmonic oscillator with a mass of 1/2 kg and a spring constant of…

A: Given: m=12kg, k=18N/m

Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: The shape of a wire of constant density w hanging under its own weight is describing by the…

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Q: of Arbitrary Constants. Formulate a differential equation that is satisfied by the following…

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Q: undetermined

A: We have to find the following conditions according to the given information

Q: Solve the non-linear Differential Equation y"=-e xy = f(x) by explicitly following these steps:…

A: Use the following formulae, to obtain the solution.

Q: Choose the right description for the given differential equation 3 Sm :) + 8 m бр? COS m + Т. %3D O…

A: The given DE is: δmδn2+δ2mδp2=cos m+T

Q: A mass-spring system damped under the influence of an external force F(t)=82cos(4t) responds to the…

A: x''+2x'+26x=82cos4tD=ddt,D2=d2dt2d2xdt2+2dxdt+26x=82cos4tD2x+2Dx+26x=0 is the auxiliary equation.…

Q: Given, (1/x^2+1/y^5)dx+(Ax+1/y^6)dy=0 is an exact differential equation. Determine the value of A.

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Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: Draw a direction field for the given differential equation and determine the behavior as ?→∞. If…

A: Given, The differential equation is  y ' = −y(5 − y).   We have to draw direction field for the…

Q: The governing differential equation for a spring-mass system is given below.  Initial conditions…

A: a) The differential equation given is x''(t)+2x'(t)+5x(t)=0, so, the characteristic equation is…

Q: An RLC circuit is modeled using the differential equation below with initial value i(n) = 20 t?i' +…

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Q: The rate of change dP of the number of wolves on an island is modeled by the following differential…

A: Let's find.

Q: The velocity v and time t are related by the first order differential equation below. Find the…

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Q: . Solve the differential equation dx 8 7. + di? 1, L are constants subject to the conditions, where…

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Q: The second order differential equation for the instantaneous position s(t) for the vibrating mass is…

A: Differential equation and it's solution

Q: A tank contains 90 kilograms of salt and 1000 liters of water. Pure water enters the tank at a rate…

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Q: A spring has mass m, spring constant k and external force F(t) with negligible damping force is…

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Q: Show that the coefficients of the given differential equation are homogencous and solve the given…

A: Given, The differentiating equation  x2+2y2dxdy=xy   and  y-1=1 We have to show the coefficient of…

Q: dx +x tan y= dy sec y 1+tan

A: The given differential equation is; dx/dy +xtany=secy/(1+tany)

Q: Consider the differential equation (DE) .7 dx2 +3 + y = sinh x + 2" a) Its i) order is ii) degree is…

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Q: The second order differential equation for the instantaneous position s(t) for the vibrating mass is…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: A second-order non-homogeneous differential equation is given by d2y/dx2 − 10 dy/dx + 21? = 21x2 +…

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Q: Solve the differential equation using modified Euler's and 4th order RK method lnx(dy/dx) + y = cot…

A: We can solve this using 4th order RK method and

Q: dy Solve the differential equation de se() by the homogeneous equation. CSC -

A: For given homogenous differential equation,             Solve by substituting y=vx

Q: . Maiko is done computing for a GS of a Differential Equation. After applying the initial condition…

A: The particular solution of a differential equation is a solution which is free from arbitrary…

Q: A large corporation starts at time t = 0 to invest part of its receipts continuously at a rate of P…

A: Start by splitting the variables and integrating each side of the equality:…

Q: The temperature of a solid at time t> 0 is modeled by the nonconstant function H and increases…

A: See the details solution below

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.