1,286 Answered Questions for the topic differential equations

Differential Equations Maths

05/31/18

How to solve exact differential equation?
Hello all!New to this Q&A thing so go easy on me please :) I'm finding difficultly solving this question. Could someone help me find the answer + show all working that would be great :)   dy... more
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Differential Equations

05/27/18

solve [x D^2 +(1-x)D-1]y=e^x
by operational factors
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Differential Equations

05/09/18

The rate of change of y with respect to t is proportional to 50-t.
 solve the differential equation
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04/28/18

Differential Equation Question Please Help.
Solve the following initial-value problem using Laplace transforms.   y''- y' - 2y = 5sin(x) ; y(0) = 1 , y'(0) = -1
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Differential Equations

04/24/18

how to reduce a second order differential equation to bessels equation
Dear expert, kindly suggest how to solve a second order differential equation by transforming it into Bessels' differential equation using a given substitution.   Eg solve: xy''+y'+y/4=0 using... more
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Differential Equations

03/27/18

Differential Equations.
I've been trying to solve this problem for hours.   Find the solution of the differential equation (ln(y))^4  dy/dx=x^4*y which satisfies the initial condition y(1)=e^2 y=?
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Differential Equations Linear Systems Vectors Calculus 3

03/25/18

Differential Equation Question
How would I write this in matrix form (x' = AX)    x' = x y' = y   Note: Is it supposed to be like this: x' = (1 v 1)(x v y) or x' = (1 + 0 v 1 + 0)(x v y)? Note: the "v" means the value after... more
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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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