Given $\frac{\partial x}{\partial t}+x^3=yx^2$, $x(0)=x_{0}$, where $x$ : $\mathbb{R}^+ \mapsto \mathbb{R}$ and $y$ : $\mathbb{R}^+ \mapsto \mathbb{R} $ with $\int_{0}^{t} y^2(s) ds <...

Given $\frac{\partial x}{\partial t}+x^3=yx^2$, $x(0)=x_{0}$, where $x$ : $\mathbb{R}^+ \mapsto \mathbb{R}$ and $y$ : $\mathbb{R}^+ \mapsto \mathbb{R} $ with $\int_{0}^{t} y^2(s) ds <...

Find the derivatives of each of the following vectors. x(t) = [ t3 - 2t2 +t etsin(t) ]

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=...

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...

Put the differential equation ty'/(t^3+7)y=cos(t)+(e^(5t))/y into the form y'+p(t)y=g(t) find p(t) find g(t)

Find the general solution to tln(t)dr/dt+r=7te^t I used integrating factor to solve it and found the answer= C/lnt+7e^t/lnt but it's wrong?

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...

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:...

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...

dy/dx =( xsquare + y + 1 ) whole square

Determine the specific solution of the following initial-value problems. y''-6y'+9y=0, y(-2)=1 and y'(-2)=0

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

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''...

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...

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

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...

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...

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 equation. 1)...

Determine the specific solution of the following initial-value problem. y''+ 4y = 0, y(pi)=0 and y'(pi)=1 My answer is: y=(0)cos(2x) + C2sin(2x) or simply y=C2sin(2x) Note:...

3y3e3xy - 1 + (2ye3xy + 3xy2e3xy)y' = 0