1,279 Answered Questions for the topic differential equations

Differential Equations Functions Derivatives Vectors

03/24/18

Differential Equation Problem. No clue how to do this.
Find the derivatives of each of the following vectors.   x(t) = [ t3 - 2t2 +t                 etsin(t) ]
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03/19/18

Differential Equation Problem: Undetermined Coefficient
Determine the specific solution of the following initial-value problems. Use the method of undetermined coefficients to find the particular solution.y'' - 2y' + 2y = x3 - 5, y(0)=6 and y'(0)=0Note:... more
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03/17/18

Differential Equation Question: 2nd Order DE. Need Help.
Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equations.   y'' - 2y' + 2y = sin(x) + cos(2x)
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03/16/18

Differential Equation: 2nd Order DFQ. Please Help
Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equation.   y''- 4y' + 4y = 2e2x+3   note: I assume Yp =... more
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03/11/18

Differential Equation: Need Help
Determine the specific solution of the following initial-value problems. y''-6y'+9y=0, y(-2)=1 and y'(-2)=0
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03/11/18

Differentials to find approximate amount of paint
A coat of paint of thickness 0.06 cm is to be applied uniformly to the faces of a cube of edge 32 cm. Use differentials to find the approximate amount of paint required for the job, correct to the... more
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Differential Equations Calculus Approximation

03/11/18

Use differentials to approximate the quantity
Use differentials to approximate the quantity a. √101 b. 4√81.6
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Differential Equations Calculus Homework Due Tomorrow

03/11/18

Differential of f
Let f be the function defined as follows.y = f(x) = √(9x+5)(a) Find the differential of f.Answer: dy = (9/2√(9x+5))dx(b) Use your result from part (a) to find the approximate change in y if x... more
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Differential Equations Verification

03/11/18

Differential Equation: Need Verification Please
Determine the specific solution of the following initial-value problem. y''+ 4y = 0, y(pi)=0 and y'(pi)=1My answer is: y=(0)cos(2x) + C2sin(2x) or simply y=C2sin(2x) Note: the "(0)" is my C1. I... more
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Differential Equations

03/06/18

How to find the general solution of xy'-4y=e^x using the associated homogeneous equation ?
so far I've done: xy'-4y=ex xyH-4yH=0 ln|yH|=4lnx+c    x4 |yH|=Ae(x^4)  y(x)=A(x)e(x^4)   y'=A'e(x^4)+4x3A(x)e(x^4)=A'e(x^4)+4x3y x(A'e(x^4)+4x3y)-4A(x)e(x^4)=e^x
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Differential Equations

03/05/18

Differential Equations.
Suppose x=c_1e^-t+c_2e^(5t) Verify that x=c_1e^-t+c_2e^(5t) is a solution to x''-4x'-5x=0 by substituting it into the differential... more
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Differential Equations

03/04/18

Differential Equations.
Given that y(t)=c1e+4t+c2e^-4t is a solution to the differential equation y''-16y=0  where c_1 and c_2 are arbitrary constants, find a function y(t) that satisfies the conditions y'' - 16 y =... more
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Differential Equations

03/04/18

Differential Equations.
let y''+6y'-16y=0a) Try a solution of the form y=e^(rx), for some unknown constant r, by substituting it into the differential equation. ...................=0b)Simplify and factor your equation in... more
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Differential Equations

03/04/18

It is easy to check that for any value of c, the function
It is easy to check that for any value of c, the function y=ce^(-2x)+e^(-x) is solution of equation y'+2y=e^-x Find the value of c for which the solution satisfies the initial condition... more
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Differential Equations

03/04/18

Solve y''=sin(x) if y(0)=0 y'(0)=3
Solve y''=sin(x) if y(0)=0 y'(0)=3   y(x)=?   I found y(x) = 1/3x-sin(x) but it says its wrong
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Differential Equations

03/04/18

setting up an integral
set up an integral for solving dy/dx=1/(x^2-16) when y(0)=0   y(x)= ...... + (integral for ..... to ......) .........     Also Evaluate your answer to the previous part to find... more
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Differential Equations Calculus Algebra

02/19/18

How to simplify this so that the c's cancel out?
dy/dx= (2cx-x^-1)/((y^-1)-2cy)   the c's are constants of integration. I am trying to find a differential equation for the family of curves: ln(xy)=c(x^2+y^2) and can't figure out the algebra to... more
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Differential Equations

02/19/18

Find the solution for the following exact differential equations.
3y3e3xy - 1 + (2ye3xy + 3xy2e3xy)y' = 0
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Differential Equations

02/17/18

Differential Equation Question
Find the solution for the following exact differential equations.   2xy^2 + 4 = 2(3 - x^2y)y' ; y(-1) = 8
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Differential Equations Calculus

02/15/18

How to find a first order differential equation for the family of curves?
y=x^(1/2)+cx   I can't seem to get the right answer :(
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Differential Equations

02/07/18

Is there some rule that x + e^c = cx ? (c is the constant of integration)
Just wondering how x^-3 + e^c = c/x^2?
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Differential Equations

02/06/18

Is in the integral of 1/x ln(x)+c or ln(x)+ln(c)?
I have seen it written the first way in some problems and the second in others. All have had correct answers. Can someone please explain why this is? Thank!
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Differential Equations Calculus

02/05/18

How to solve the differential equation with substitution?
y'=(x^2-y^2)xy, with y(1)=2
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Differential Equations

12/08/17

How do I solve the differential equation x-4y(x)*y'(x)*(x^2+1)^(1/2)=0 with the initial condition: y(0)=10.
When I solve it with separation I get to a point where y^2=5/2(x^2+1)^(1/2)+C but then I get two solutions and then my equation gets messy when trying to solve for the constant C with the initial... more
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Differential Equations Numerical Analysis Taylor Series

11/07/17

Numerical solver for y’=3xy^3
For this equation is the Taylor Series the best approach to wstimate numerically? I am also using Euler’s to compare.    Trying to find y(1) given y(x) is a solution to the equation and knowing... more
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