Differential Equations Answers

y′+(cotx)y=xcscx,y(^/2)=1
o y=−x^2/2sinx−1−π^2/8 sinx
y=x^2/2sinx+1−π^2/8/sinx
y=−x^2/2sinx+1+π^2/8/sinx
y=−x^2/sinx−1−π^2/8/2sinx

Obtain a solution of the wave equation
D2u(x,t)/dt2 = 16*d2u(x,t)/ dx2
For 0<= x<= π and t>0, and the following boundary and initial conditions:
U(0,t)=u(π,t)=0,
U(x,0)=x(π-x) and du(x,0)/dt =0

Reduce the following PDE to a set of three ODEs by the method of separation variables.
1/r d/dr(r dv/dr)+1/r2 d2v/dϴ2+d2v/dz2+k2v=0

Charging characteristics for a series capacitive circuit is:

Vc=〖V(1-e〗^(-(t/T))), where T=CR
time is constant
Capacitor C= 100nF
Reisistor R=47kΩ
Supply Voltage, V= 5 Volts

1. Determine the value of (t) when vc =4.15 volts.
2. Differentiate the charging equation and find the rate of change of voltage at 6 ms

y′−ay=0,y(x0)=y0
• y=−y0e^−ax0e^−ax
• y=y0 e^ax0 e^−ax
• y=−y0 e^−ax0 e^ax
• y=y0 e^−ax0 e^ax

x=2py + y^2p^3

Solve ∂^2U/∂x^2=9(∂^2U/∂x^2)

1. Cos(3x - y)
2. x^2 + y^2
3. Sin (3x - y)
4. e^-3/pix Sin(piy)

one hundred grams of cane sugar in water are being converted into dextrose at a
rate which is proportional to the amount unconverted find the differential equation expressing the rate of conversion after t minutes

a particle of mass m falls freely under gravity in a liquid that offers a resistive force proportional to its velocity : fres= -gama dx/dt solve it.

10. The degree of differention Equation
(d^3y/dx^3)^2 +2 d^2y/dx^2 − dy/dx + x^2(dy/dx)^3 = 0 is _________
a. 2, b 1, c. 3, d. 4