Write the differential equation, and solve it. A 120-gallon (gal) tank initially contains 90 lb of salt dissolved in 90 gal of water. Brine containing 2 lb/gal of salt flows into the tank at the rate of 4 gal/min, and the well-stirred mixture flows out of the tank at the rate of 3 gal/min. How much salt does the tank contain when it is full?

Q: y" – 2y' + y: [12x – 4]e-Sx %D -

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Q: The order of the differential equation: ( d*t )2– 5(- dr 10 10 dr - )3 + xt = 0 is

A: The order of a differential equation is defined as the highest derivative present in the…

Q: e-(x²+y³)(x dx + y dy) = 0

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Q: Solve the differential equation. 4. y" + 8 y' + 16 y =0

A: Solution:Giveny''+8y'+16y=0To find the differential equationFormula:If α has double rootCF=eαx(Ax+B)…

Q: Write the the differential equation by separating the variables. - = x-y dx

A: Solve the following: dydx=x-y .................. (1) Let us put, x-y=t Differentiating both sides…

Q: yp²_2xP+Y =o X 0:

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Q: solve the differential equation   x(4ydx+2xdy)+y3(3ydx+5xdy)=0

A: Given that the differential equation is    x(4ydy+2xdy)+y3(3ydx+5xdy) = 0

Q: 10. (Dª + 8D² + 16)y = 0 4

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Q: - ydx + (x ++ Vxy )dy = 0

A: Given  -ydx+(x+xy)dy=0 To find solution of this Differential Equation:

Q: Solve the differential equation by variation of parameters. 1 y' + 3y' + 2y 6+e*

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Q: 3 X' -3 5

A: This question related to system of ode.

Q: Solve the differential equation dR a(R + 9). dz

A: Given differential equation  dRdx=aR2+9dRR2+9=adx Integrating both sides, we get…

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

A: This question is about application of differential equation

Q: Check that the differential equation is linear and find the general solution Y'-(6/X)Y = x^4

A: Given differential equation is y'-6xy=x4 which can be written as dydx-6xy=x4. We have to check…

Q: Solve the differential equation. (Assume the independent variable is x.) y" + 3y = 0

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Q: - = y? + xy dx

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Q: determine whether the given differential equation is exact. If it is exact, solve it.

A: As per our guidelines we are supposed to answer only one question.kindly repost other question as…

Q: solve the differential equation (x3+y4)dx+8y3xdy=0 when x=4, y=1/2

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Q: Calculate whether the differential equation is exact or not and Find the general solution.

A: The given differential equation is:x2+2x+ydx+2dy=0We need to check whether the equation is exact or…

Q: Solve the differential equation  P3x-p2-y+1=0

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Q: 3. my²dx + m?ydy = 0

A: The simplification of the given equation helps to find the solution of the equation. Simplify the…

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: Find the differential equation having the solution as: a. y = C,e¬x + C2e¬2x + x b. y = C, + C2e³x

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Q: y' + 5xey = 0

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Q: Find the order of the differential equation. And check if it is linear or nonlinear.

A: Given the differential equation

Q: Determine whether the differential equation (5.a2 – 2xy + 4) dr + (2y² – x² + 5) dy = 0 - is exact.…

A: The given differential equation is 5x2-2xy+4dx+2y2-x2+5dy=0

Q: Solve the differential equation 3y' = x + y by making the change of variable u = x + y.

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Q: Solve the differential equation,  x⁴ y' = -x³y - csc (xy)

A: Given, x4y' = -x3y -csc(xy)⇒y' = -x3y -csc(xy)x4                    1substituting y =ux , u is a…

Q: Solve for the general solution of the differential equation : ( D + 100 ) y = 0

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Q: (D² - 1)y= 2 1+ex

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Q: Q:: Solve the differential equation to

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Q: Solve the differential equation: p3-4xyp+8y2=0

A: Given differential equation p3 - 4xyp + 8y2 = 0                                             (1)…

Q: = (+ Use the fact that i and -i = to solve the differential equation dx4 + y = 0.

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Q: . Solve the differential equation d²y + y = csc x dx2

A: We have to find out

Q: Solve the differential equation 9y' = x + y by making the change of variable u = x + y.

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Q: . (D² + *. + D)y = 6 + 3 e²

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Q: Solve the differential equation y? 3x dr

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Q: solve the differential equation for p x + 2(xp-y) + p^2 = 0

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Q: -3z y" + 6y' + 9y = for a> 0.

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Q: Solve the differential equation: (p+2x)(p+y+x)(xp+y+x)=0

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Q: solve the differential equation and express final answer with the value of C (3x^2 +y^2) dx + 2xydy…

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Q: x2 + 2x + 1 y' = y +2

A: The given differential equation is: dydx=x2+2x+1y+2 We can solve this ODE by using separation of…

Q: Determine whether the given differential equation is exact. If it is exact, solve it.

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 19. (5x2 — у) dx + xdy %3D 0

A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

Q: x²(y+: x(2y+

A: The differential equation is x2y'=4x2+7xy+2y2. Divide by x2 on both sides, y'=4+7yx+2yx2 Substitute…

Q: Solve the differential equation by variable separable r®y² dæ

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Q: dH RH² /1 + R² dR In H

A: Given dHdR=RH21+R2lnH

Q: Solve the differential equation y' – 2y = x²e3z

A: Given y'-2y = x2e3x It is the first order linear differential equation Compare it with y'+Py = Q…

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.