Dt/dt = (h + bT)(T∞ − T), T(0) = To   To=1800K T∞=300K h=.025 b=10^-5 Find the explicit solution of the IVP

Q: 4/3 5² = 2² -3 (2²) *² y' x

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Q: Solve the inhomogeneous 1st order equation Ux − Ut = cost U(x, 0) = 0.

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Q: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

Q: Find dy/dt and d^2y/dt^2 for function aln(y)+b cos^2(ty)=2t^3 where a  and b are certain constants.

A: Derivative two times simultaneously and use the forma for derivative

Q: Solve the inhomogeneous 1st order equation U₂ - U₁ = cost U(x, 0) = 0.

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Q: ctan x (2) Let h(x) = t dt, calculate h'(T/3). ww. t2 + 2

A: Solve the following

Q: Solve DE (1+e** )ax +e x/y 1 dy=0

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Q: Find all the solutions for e^(iz)+1-i=0

A: The given function is to find the solution for the given complex function equation. Given complex…

Q: Sve SVé -3 dt u = Ve' – 3

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Q: Suppose f(x) = "6r V1+f dt.

A: Topic = Integration

Q: Jse variation of parameters to find a solution o the given system: dx/dt%3D2Y+2…

A: Given system isdxdt = 2y+2 ; dydt = -x+3y+e-3t ; can be reduced asx'y' = 02-13xy+2e-3tis of the form…

Q: P= pvo'smax A sin (kx-mt) = pvw²s

A: Given function  P=ρvω2smax2Asin2kx-ωt

Q: What is general solution of v = ds/dt if v = 2/t^3/2? a.-4/t^1/2 = s^2 + c b.-4/t^1/2 = s + c^2…

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Q: -1 Find L s2–18s+40 s(s²–6s+10) |

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: find a particular solution to: y''+5y'+4y=8te^(2t)

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Q: Solve for the general solution: x2y" - xy' - 3y = 0. Oy=c1 x + c2 x^3 Oy=c1 x + c2 x^(-3) Oy=c1…

A: Topic = Differential equation

Q: Solve 2cos^2(t)+3cos(t)+1 = 0` for all solutions 0 <= t < 2pi'.

A: To find solutions for the given equation substitute cos(t) = x amd convert the given equation in to…

Q: y'=-3y ; y(0)=4

A: y′=−3y;y(0)=4

Q: How do I use the Bernoulli sub for the eq:   (  x^2 ) (dx/dt)= x^2t+3x^3 and where x( 0) =2 thanks…

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Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

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Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

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Q: Find ect and the solution to X' = CX + (1) t X (0) = 0

A: X'=CX+1t1X0=000

Q: Find dx/dt, dy/dt, dy/dx for  x=9t-9ln(t), y=6t^2-6t^-2

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Q: (T^2-x)dt-tdx =0 when t=1 x=5 Ans,: x=1/3t^2 + 14/3t please show solution

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Q: Fnd the solution to the initial value problem: dy/dt = (2t)/(y+t^(y)), y(0) = -2

A: Here the question should be , dy/dt=(2t)/(y+(t^2)y ) , y(0)=-2. I have solved it accordingly .…

Q: Use the separation of variables to find the general solution to dy/dt = (3t + 2)*y^(4) Be sure to…

A: We have to find the general solution to the differential equationdydt=(3t+2).y4

Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: y'-2 xy=2 y (0)=1

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Q: Y"+3y'+2y= 1/(3+e^x)   solve the DE by variation of parameters

A: We have to use Variation of Parameter Method to find General solution of given DE.

Q: e'dy + (5t + ye')dt = 0.

A:

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.