Page 163 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 8.6 Keywords

Exact Differential: An equation

Pdx Qdy Rdz 0, ...(1)
is an exact differential if its integral is found in the form
( , , )u x y z , c (c being a constant)

Exact Differential Equation: When equation (1) is put into the form

y
x
du ( , , ) Pdx Qdy Rdz 0,
z
it is called Exact Differential Equation
Integrable: A differential equation when solved is said to be integrable.
8.7 Review Questions

dx dy dz
1. Solve
x y z

2. Solve yz log y dx z x log z dy xy dz 0
3. Solve (y b )(z c )dx (x a )(z c )dy (x a )(y b )dz 0

4. Solve yz 2 (x 2 yz )dx zx 2 (y 2 xz )dy xy 2 (z xy )dz 0

dx dy dz
5. Solve 2 2 2
y x xyz (x y )

Answers: Self Assessment

2
3. x y cze 2 , (c being a constant)
4. (a 2 x 2 y 2 1/2 C , Z (c being a constant)
)

5. xy 2 cz 3 , (c being a constant)

6. (x z ) 2 ( c y z ) (c being a constant)

7. ( z x y ) y 2 cz 2 (c being a constant)

8. x 2 y 2 z 2 cx (c being a constant)

9. xy ( c a z ) (c being an arbitrary constant)

10. xy yz zx ( c x y z ), (c being a constant)

6t
11. x e (A cos t + B sin t)
t
y e 6t [(A B )cos t (A B )sin ]

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