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Find the Laplace transforms of the following function:
- L{t^2sinkt}
Form the partial differential equation by eliminating the function ϕ and Ψ from z=ϕ(x+iy) +Ψ(x-iy)
(D+1)x- Dy=-1
(2D-1)x-(D-1/2y=1
a chip is placed at room temperature of 40°c after minutes its temperature changes from 80c to 60c the proportionallity constant in case is k=0.05 ln2 find temperture of chip after 40 minute.
Use the Laplace transform to solve the given initial-value problem.
y′ + 2y = sin 4t, y(0) = 1
Solve
"u_t=u_{xx}" and boundary conditions are "u_x(0,t)=u(1,t)=0".
Higher order linear ordinary differential equation
• Homogeneous linear ODE
• Homogeneous linear ODE with constant cofocient
• Non homogeneous linear ODE
Solve x2 dy/dx = y2 - xy. given that y = 1 when x = 1
The rate of increase of the population of bateria in a culture is proportional to the number of bacteria at any given instant. Assume the initial count of bacteria is 1000 and after 1 hour the amount is 1200. Find (i) the number of bacteria present immediately after 5 hours. (iii) the time lapse before the number reaches 4000
Find the general solution of the DE(y^2-2xy+6x)dx-(x^2-2xy+2)dy=0
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#340153 on Dec 2023