Advanced Engineering Mathematics — Summer 2018

dy Solve  exy x2eyby variable separable method. dx

dy Solve  ysinx  ecosx dx

 1 State convolution theorem and hence find L1     s2 4 2  

Solve y"3y'2ye3x

Find Fourier series for f(x)  x2;  x  

Find Fourier series in the interval  0,2  if   0 x   f(x)   x  x  2  1 2 and hence show that    2n1 2 n1

Find the series solution of y"x2y0 about an ordinary point x 0

Solve y'''6y''11y'6y0  

Solve D2 9 y cos4x

Solve y"4y4tan2xby method of variation parameter.

 1  Find L1     s1 s2 

Solve y''2y'5y 5x3 6x2 6xby method of undetermined coefficients.

Find the series solution of 8x2y"10xy'1xy0  

Solve x4 y4 dxxy3dy 0

Express sinx as cosine series in 0 x  

Find Fourier series for f(x) eax in  0,2  ; a  0

 

Find Lcos2 t  

Find Le2t sin3t

Solve y"ysin2t;with y(0)2, y'  0  1 by using Laplace transform.

Solve p2 q2 1

Solve xpyq3z

2z z 2z Solve 4 4 e2x3y x2 xy y2

Solve p2 q2  xy

3z Solve cos  2x3y  x2y

Solve by Charpit’s methodp  zqy 2