1,272 Answered Questions for the topic differential equations

Differential Equations Calculus

10/31/21

y'' - xy' + 2y = cosx
Solve the following non-homogeneous ODE using a power series expansion centered at 0. Listing the first four nontrivial terms for y1 and y2.
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Differential Equations

10/31/21

Charlie is selling three different types of chocolate boxes:
Charlie is selling three different types of chocolate boxes: Price: $32 Price: $34 Price: $28Life is like a box of chocolates and Valentine's day is coming up. Charlie plans to offer a special... more
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Differential Equations Calculus

10/28/21

How do you solve dy/dx=y/x using homogeneous substitution?
I am aware the answer is y=Ax where A is a constant, and I know how to solve it using separable variables and integrating factor. I would like to know how to solve it specifically through the... more
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Differential Equations

10/28/21

Diff. Eq. Tank Problem
A very large tank initially contains 100L of pure water. Starting at time t=0 a solution with a salt concentration of 0.5kg/L is added at a rate of 6L/min. The solution is kept thoroughly mixed and... more
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Differential Equations Calculus

10/28/21

How to solve dy/dx=y/x using homogeneous equation if the answer is y=Ax where A is a constant?
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Differential Equations

10/27/21

How much kg of salt is in the tank after 30 minutes?
A very large tank initially contains 100L of pure water. Starting at time t=0 a solution with a salt concentration of 0.5kg/L is added at a rate of 6L/min. The solution is kept thoroughly mixed and... more
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Differential Equations Math

10/27/21

Find y as a function of x if :
Find y as a function of x if :y′′′−5y′′−y′+5y=0,y(0)=−4,  y′(0)=−9,  y′′(0)=92. y(x)= ____________
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Differential Equations Math

10/27/21

A tank contains 2960 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 L/min, and is thoroughly mixed into it.

A tank contains 2960 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 L/min, and is thoroughly mixed into it. The new solution drains out of the tank... more
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Differential Equations Math

10/27/21

A thermometer is taken from a room where the temperature is 25oC to the outdoors, where the temperature is 3oC. After one minute the thermometer reads 14oC.
A thermometer is taken from a room where the temperature is 25oC to the outdoors, where the temperature is 3oC. After one minute the thermometer reads 14oC. (a) What will the reading on the... more
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Differential Equations

10/26/21

differential equations

A very large tank initially contains 100L100L of pure water. Starting at time 𝑡=0t=0 a solution with a salt concentration of 0.5kg/L0.5kg/L is added at a rate of 6L/min.6L/min. The solution is kept... more
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Differential Equations

10/26/21

Differential equations

A Bernoulli differential equation is one of the form 𝑑𝑦𝑑𝑥+𝑃(𝑥)𝑦=𝑄(𝑥)𝑦𝑛.dydx+P(x)y=Q(x)yn.Observe that, if 𝑛=0n=0 or 11, the Bernoulli equation is linear. For other values of 𝑛n, the... more
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Differential Equations Calculus Derivative

10/26/21

If f ( x ) = 20 , find f ' ( 5 ) .
any help would be amazing thanks
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Differential Equations

10/25/21

The term M(x,y)dx+N(x,y)dy becomes an exact differential if the left hand side above is divided by y^7. Integrating that new equation, the solution of the differential equation is

The differential equationy−4y^7=(y^6+6x)y′can be written in differential form:M(x,y)dx+N(x,y)dy=0whereM(x,y)= , and N(x,y)= .The term M(x,y)dx+N(x,y)dy becomes an exact differential if the left... more
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Differential Equations

10/25/21

A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n. y(x)=?
A Bernoulli differential equation is one of the formdy/dx+P(x)y=Q(x)y^n.Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^(1−n) transforms... more
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Differential Equations

10/25/21

Differential Equation
A 120-gallon tank initially contains 80 lbs. of salt dissolve in 90 gal of water. Brinecontaining 2lbs/gal of salt flows into the tank at the rate of 5 gal/min, and the mixtureflows out of the tank... more
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Differential Equations Calculus

10/21/21

Calculus (Differntial Equation)
Prove that this equation Y-3 =x³(3ex+C) is a solution of the given differential equation which is xy'+y+x⁴y⁴ex=0
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Differential Equations Calculus

10/21/21

Calculus 3 (Differential Equation)
Prove that each equation is a solution of the given differential equation:Y-3 =x³(3ex+C) ; xy'+y+x⁴y⁴ex=0
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Differential Equations Calculus

10/21/21

Calculus 3 (Differential equation)
Prove that each equation is a solution of the given differential equation: In y = C1ex + C2e-x ; yy’’- (y’)² = y² In y
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Differential Equations Calculus

10/19/21

Let = tan(5x + 3) Find the differential dy when x = 5 and dx = .3 Find the differential dy when x = 5 and dx =.6
Let = tan(5x + 3)Find the differential dy when x = 5 and dx = .3Find the differential dy when x = 5 and dx =.6
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Differential Equations Calculus

10/19/21

Let y = 3x2 Find the change in y, Δy when x = 5 and Δx = .2 Find the differential dy when x = 5 and dx = .2
Let y = 3x2Find the change in y, Δy when x = 5 and Δx = .2Find the differential dy when x = 5 and dx = .2
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Differential Equations Mathematics

10/17/21

Solve the given differential equation y(u ^ 2 + 2)du - (u ^ 3 - u)dy = 0
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Differential Equations

10/15/21

In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+4y=12te−2t−(8t+12) with initial values y(0)=−2 and y′(0)=1.
Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients. FindY =Y' =Y" =
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Differential Equations

10/15/21

Find y_p and the specific solution for y"-3y'-4y=3e^(2t) with y(0)=0 and y'(0)=0

Find y_p and the specific solution for y"-3y'-4y=3e^(2t) with y(0)=0 and y'(0)=0
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Differential Equations

10/11/21

In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+4y=12te−2t−(8t+12) with initial values y(0)=−2andy′(0)=1.
In this problem, you will use undetermined coefficients to solve the nonhomogeneous equation y"+4y'+4y=12te^(-2t)-(8t+12) with initial values y(0)=-2 and y'(0)=1.  Write the form of the particular... more
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Differential Equations Math Calculus

10/08/21

How could I solve it? someone help me with the integration limits, please
find all solutionsy'+2y=b(x) 1 − |x|, if |x| ≤ 1 b(x) = 0, if |x| > 1using this formulay = e-2x∫ e2xb(x)dxHow could I solve it? someone help me with the... more
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