x''+3y'+3y=0 , x''+3y=te^-t, x(0)=8 , x'(0)=2 , y(0)=0

Use Laplace transform to solve the system, with the given initial conditions. x''+3y'+3y=0 and x''+3y=te^-t x(0)=8 x'(0)=2 and y(0)=0

laplace transform of the piecewise function y' -3y = {3, 0<= t< 1; 0, 1<=t}, y(0) = 2

Find laplace transform of the piecewise function y' -3y = {3, 0<= t< 1; 0, 1<=t}, y(0) = 2

inverse laplace transform of (9s-3) / ((s-3)^2 +9)

Find the inverse laplace transform of (9s-3) / ((s-3)^2 +9)

inverse laplace transform of (3s-15) / (s^2 - 8s + 20)

Find inverse laplace transform of (3s-15) / (s^2 - 8s + 20)

y'' +4y = {4, 0 <= t< 1; 0, 1 <= t} y(0) = 3 y'(0)= -2

find the inverse laplace transform of the piecewise differential equations y'' +4y = {4, 0 <= t< 1; 0, 1 <= t} y(0) = 3 y'(0)= -2

x' = -6x - 4y , y' = -3x - 10y

find the general solution of x'=-6x-4y and y'=-3x-10y

2p'' - (2*sqrt(2Pi+2))p' +(Pi+1)p = 0

Solution

y'' - (1/x^2) y' +(1/x^3) y = 0

Solution

x' = y - x + t , y' = y , x(0)=6 , y(0)=8

Find the solution to 

x' = y - x + t
y' = y
if x(0)=6 and y(0)=8

y''''-9y=0 , y(0)=1, y'(0)=0, y''(0)=0, y'''(0)=1

Use Laplace transform to solve the initial value problem y''''-9y=0 , y(0)=1, y'(0)=0, y''(0)=0, y'''(0)=1

y''-6y'+5y=te^t y(0)=2, y'(0)=-1

Solve for Y(s), the Laplace transform of the solution y(t) to the given initial value problem
y''-6y'+5y=te^t y(0)=2, y'(0)=-1

dy/dx = 3e^(2x) , y(0) = 5/2

dy/dx = 3x^2 y^2 - y^2

Find the general solution to the differential equation
dy/dx = 3x^2 y^2 - y^2
Find the particular solution for which y(0) = 1 ie when x = 0 , y =1

dy/dx = (x - y)/x

dy/dx= sin(3x)/x^2 - 2y/x

dy/dx + y = x

y'' + 8y' + 25y = 0 , y(0) = 1 , y'(0) = 8

Find the complete solution to the homogeneous differential equation below. For those differential equations that include initial conditions evaluate the constants in the solution
y'' + 8y' + 25y = 0 , y(0) = 1 , y'(0) = 8

Particular Solution of 3y'' + y' + 2y= 5t + 2

Find particular solution of 3y'' + y' + 2y= 5t + 2

Inverse Laplace Transform s^2/(s+1)^3

Find Inverse Laplace Transform of s^2/(s+1)^3 using partial fractions

y'' + 2y' + 24y = 8cos(4x)

Find the general solution of the differential equation y'' + 2y' + 24y = 8cos(4x)

dy/dx = 1/(x^2 - 3x) , y(4) = (2/3) ln(4)

Solve the initial value problem and give the interval of definition.
dy/dx = 1/(x^2 - 3x) , y(4) = (2/3) ln(4)

dy/dx = x/y + y/x +1

Solve the given differential equation.
dy/dx = x/y + y/x +1

dy/dx = (-2x^3 - 2y)/(6x - y^4)

Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose level curves are solutions to the differential equation dy/dx = (-2x^3 - 2y)/(6x - y^4)

y'' - 2y' = e^t/(t^2 + 1)

Solve y'' - 2y' = e^t/(t^2 + 1) using Variation of Parameters

dy/dx= xy + 7x +2y + 14

dy/dx= xy + 7x +2y + 14

Fundamental set of solutions (Wronskian)

Find a fundamental set of solutions for y'' + 2y' + 10y = 0

Inverse Laplace Transform of 1/(s^2 - 8s + 17)

Find inverse laplace tranform of 1/(s^2 - 8s + 17)