1,280 Answered Questions for the topic differential equations

Differential Equations

11/10/21

Using matrix algebra, find a general solution to the following system of equations x' = 3x - 4y and y' = 4x - 7y

Using matrix algebra, find a general solution to the following system of equations: x' = 3x - 4y y' = 4x - 7y The general solution functions are: ( use c1 and c2 as the constants and enter the... more
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Differential Equations Math Text Task

11/10/21

If they worked alone, how long would each of the workers take to finish the work?
Two workers were given some work. When the first one had worked for 7 hours and the other worker for 4 hours, It turned out, that in total they had done 5/9 of total work. Nowthey worked together... more
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Differential Equations

11/09/21

What is the scalar multiple to make the matrices match?
What is the scalar multiple that will make the 2x1 matrices of [ i, 1] and [ -i, 1] match?
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Differential Equations

11/08/21

What is the scalar multiple to make the matrices match?
What is the scalar multiple that will make the 2x1 matrices of [ i, 1] and [ -i, 1] match?
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Differential Equations Math Calculus Advance

11/07/21

Math Question (Advanced!!!) Please solve it for me. I am so stuck.

Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis, and a tangent line to the graph of f=(x+5)^-2.
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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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