Page 106 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Unit 5: Differential Equations

5.5 Keywords Notes

dy
The first order differential equation is an equation when the relation between x, y involves
dx
only. The degree of differential equation is the highest power of its derivatives.
The Linear differential equation is an equation involving linear power of independent variable.

5.6 Review Questions

1. The equation of a parabola is

y 2 4a x b
where a and b are constants form a differential equation

2
2. If x 2 y 2 a , prove that
dy x
dx y
3. The equation of a straight line is
y mx c

show that its differential equation is

2
d y
2 = 0
dx
4. Solve by the method (A)
ydx xdy xydx

5. Show by the method (B), the solution of

xdy ydx 1 x
xdx ydy 0, is x 2 y 2 2tan K (K being a constant)
x 2 y 2 y

Answers: Self Assessment

2
d y 2
1. 2 w y 0
dx
dy 2 x
2. x y x x 1 e 0
dx
3. The equation is of second order, second degree non-homogeneous and non-linear.

2
d y dy
4. 2 2 2y 0
dx dx
a
5. y ae sin x , being an arbitrary constant.

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