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Solve the following differential equations: (x^3+y^3)=(xy^2)dy/dx
The ends of P and Q of a rod have the temperature at 30C and 80C until steady state situations prevail the temperature of the ends are changed to 30 C and 60 C respectively find the temperature distribution in the rod time
2uxx + 2xyuxy + 2x
2uyy + xux = 0
Classify each of the following equations and reduce it to canonical form
Find the solutions of xux +(y+x2)uy= u satisfying u(2,s)=s-4
Activity 1:
Solve the following problems applying the concepts learned above. Write your answer on a separate sheet of paper. (Show your solution)
1. The rate of change x is proportional to x. When t =0, x0 = 3 and when t =2, x=6. What is the value of x when t =4?
2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately 15% of the original amount decomposes in 100 years. How much amount of the substance has decayed after 600 years? Also, find the half - life t1/2 of this radioactive substance ; that is, find the time required for this substance to decay to one- half of its original amount.
(6x+yz)dx+(xz-2y)dy+(xy+2z)dz=0
(x²D²-xD+4)y=cos(logx)
integrating factor by inspection (2x^2 + y)dx + (x^2y - x)dy = 0
integrating factor by inspection (2x^2 + y)dx + (x^2y - x)dy = 0
xyp+y^2q=2xy-2x^2
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