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Differential Equations
look at the partial differential equation
xux - tut= u
show that u( x , t) = xf( xt) is a general solution , where f is any differentiable function
xux - tut= u
show that u( x , t) = xf( xt) is a general solution , where f is any differentiable function
Differential Equations
solve the wave equation c^2 uxx = u tt for t ≥ 0 0 ≤ x ≤ π . Take c = 1 , take initial and boundary conditions
u(x , 0) = sin x and ut(x , 0) = 0
u( 0 , t) = u ( L , t ) =0 ?
u(x , 0) = sin x and ut(x , 0) = 0
u( 0 , t) = u ( L , t ) =0 ?
Differential Equations
use the laplace transform to solve the follwing initial value problem
y''-y'-6y=-6t+11 , y(0)=-1 y'(0)=4
y''-y'-6y=-6t+11 , y(0)=-1 y'(0)=4
Differential Equations
Given the Unconstrained Function,
F = x₁² + 1/x₁ + x₂ + 1/x₂
Using the direction of the steepest descent, update the design by the standard formula: x¹ = x⁰ + αS¹
F = x₁² + 1/x₁ + x₂ + 1/x₂
Using the direction of the steepest descent, update the design by the standard formula: x¹ = x⁰ + αS¹
Differential Equations
y*(Zxx )+ (x + y)*(Zxy)+ x*Z(yy)= 0, (y is not equal to x).
Find the general solution for partial differential equation.
Here Z(xx) is partial derivative of respect to Z. Similarly for z(xy, and z(yy)...
Find the general solution for partial differential equation.
Here Z(xx) is partial derivative of respect to Z. Similarly for z(xy, and z(yy)...
Differential Equations
At 1:00 pm a ship is 30 miles east of the harbor sailing in at 10 mph. Another ship has just left the harbor sailing south at 40 mph. When will the two ships be the closest?
Differential Equations
show that given equation is homogeneous and solve
(x^2+xy)dy=(x^2+y^2)dx
(x^2+xy)dy=(x^2+y^2)dx
Differential Equations
I am looking for assistance in starting to solve this problem. Dont need the answer but a methodology for figuring it out on my own. A particle moves from right to left along the parabolic curve y = square root of -x in such a way that its x coordinates decreases at the rate of 4 meters per second. How fast is the angle of inclination in degrees of the line joining the particle to the origin changing when x = -2?
Differential Equations
find the laplace transform of
1) f(t)=(1+te^-t)^3
1) f(t)=(1+te^-t)^3
Differential Equations
what is the derivative quotient of 6x-5/2x-1
