Tutorial-1
1.
Find the
differential equation of family of curves 
where 
where
2.
Form
differential equation of the cardiod 
3.
Find the
differential equation of all parabolas with x-axis as the axis and (a,0) as
focus
4.
Solve 
5.
Solve 
6.
Solve 
7.
Solve 
8.
Solve 
9.
Solve 
Tutorial-2
1.
Solve 
2.
Solve 
3.
Solve 
4.
Solve 
5.
Solve 
6.
Solve 
7.
Solve 
8.
Solve 
9.
Solve 
10. Solve 
Tutorial-3
1.
Solve 
2.
Solve 
3.
Solve 
4.
Solve 
5.
Solve 
6.
Solve 
7.
Solve 
8.
Solve 
9.
Solve 
10.Solve
Tutorial – 4
1.
Verify
that the functions 
and 
form a basis of solution of 
and then solve it when 
and 
and form a basis of solution of and then solve it when and
2. Find the
general solution of 
where one of the solution is 
where one of the solution is
3. Solve 
where 
is one of its solution.
where is one of its solution.
4. Solve 
; 
;
5. Solve 
6. Solve 
7. Solve 
8. Solve 
9. Solve 
10. Solve 
where 
and 
where and
11. Solve 
12. Solve the following differential
equations by Method Of Variation of
Parameters
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
Tutorial-5
Ø Solve
the following differential equations
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
Ø Solve
the following differential equations by Method of Undetermined Coefficients
1. 
2. 
3. 
4. 
Tutorial-6
Ø Solve
the following differential equations
1. 
2. 
3. 
4. 
5. 
6. 
Ø Find
the Series solution of 
Ø Solve 
by Poer series method
by Poer series method
Ø Find
the Series solution of 
around an ordinary point 
around an ordinary point
Tutorial 7
1.
Find
the Fourier series for f(x) = x cos
x in (0,2
) and (-
,
).
) and (-,).
2. Find the Fourier series for 
and Hence
deduce that 
and Hence
deduce that
3.
Obtain
Fourier series for
(-
< x < 
).
(- < x < ).
4. Obtain
Fourier series for
in –
< x <
.Hence show
that
in – < x < .Hence show
that
(i) 
(ii) 
(iii) 
(ii) (iii)
5.
Obtain
Fourier expansion for 
6.
Obtain
Fourier series for 
7.
Obtain
Fourier series for 
and Hence
deduce that 
.
and Hence
deduce that .
8.
Find
Fourier series for 
in the range 
in the range
9. . Find
the Fourier series of the periodic function f(x).
and hence
Deduce that 
.
10. Obtain Half-range sine
& cosine series for 
11. Find the half- range
cosine series for f(x) = 
in 0 < x
< 1 and
in 0 < x
< 1 and
Hence deduce that ( i)
(ii) 
(ii)
Tutorial 8
1.
Find
the Laplace Transform of the following. Show the detail of your work
(i) sin 
t
(ii) cos 
t
(iii) 
t
(ii) cos t
(iii)
(iv)
(v) 
(vi) 
(v) (vi)
2.
Find
the Laplace Transform. (Show the detail)
(i) 
(ii) 
(iii)
(ii) (iii)
(iv)
(v) 
(vi)
(v) (vi)
3.
Find
the Laplace Transform of the following,
(i) 
(ii) 
(iii) 
(ii) (iii)
(iv)
(v)
(vi) 
(v)
(vi)
(vii)
(viii) 
(ix) 
(viii) (ix)
4.
Find
the Laplace Transform of the following functions
(i) 
(ii) 
Tutorial-9
1.
Find
the Inverse Laplace Transform of the following. Show the detail of your work
(i) 
(ii) 
(iii) 
(ii) (iii)
(iv)
(v) 
(vi) 
(v) (vi)
(vii)
(viii) 
(viii)
2.
Find
the Inverse Laplace Transform of the following functions
(i) 
(ii) 
(ii)
(iii) 
(iv) 
(iv)
(v) 
(vi) 
(vi)
3.
Find
the L.T. of the following. (Differentiation of L.T. method)
(i) 
(ii) 
(ii)
4.
Find
the I.L.T. of the following
(i) 
(ii) 
(iii) 
(ii) (iii)
Tutorial
– 10
1.
Find
the L.T. and I.L.T. of the following. ( Integration of L.T. method)
(i) 
(ii) 
(iii) 
(ii) (iii)
2.
Find
the I.L.T. of the following. (Division by power of s method)
(i) 
(ii) 
(iii) 
(iv) 
(ii) (iii) (iv)
3.
Prove
that ,
then
then 
4.
Evaluate
(i) 
(ii) 
(ii)
5.
Show
that 
6.
Solve
the following initial value problems
(i) 
(ii) 
(i) 
7.
Solve the given problems
(1) 
(2) 
(3) 
(2) (3)
(4) 
(5) 
(6) 
(5) (6)
(7) 
(8) 
(9) 
(8) (9) 
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