Solve (y2−x2)dx+(2xy)dy = 0
[3 marks]Solve x2dy +xy = x4y6 dx
[4 marks]Solve y′′ +2y′ +5y = e−tsint, y(0) = 0,y′(0) = 1 using Laplace transform.
[7 marks]d4y Solve +4y = 0. dx4
[3 marks]Solve y′′ +4y = sin3x.
[4 marks]Find the Fourier series of f(x) = x +x2 in −𝜋 < x < 𝜋.
[7 marks]Find the Fourier series for the function −𝜋 ; −𝜋 < x < 0 f(x) = { . x ; 0 < x < 𝜋
Find L{sin (3t+2)}.
[3 marks]Find L−1{ 1 }. (s+1)(s2+1)
[4 marks]Find the power series solution of y′′ +x2y = 0.
[7 marks]Find L{t sinℎ 3t}.
[3 marks]Find L−1{tan−1( 2 )}. s
[4 marks]Using the method of variation of parameters, solve y′′ −4y′ +4y = e2x . x
[7 marks]Solve y′′ +6y+9y = e3x.
[3 marks]Solve (D3 −D2 −6D)y = x2 +1.
[4 marks]Using convolution theorem find the inverse Laplace transform of1 . (s2+a2)2
[7 marks]Find the convolution of t and et.
[3 marks]cosat−cosbt Find the Laplace transform of . t
[4 marks]Find the Fourier series for the function f(x) = 2x −x2 with period in the range (0, 3).
[7 marks]Solve z = px+qy+√1+p2 +q2.
[3 marks]Solve p(1+q) = qz.1
[4 marks]𝜕2z 𝜕2z Solve −4 = cos2xcos3y. 𝜕x2 𝜕y2
[7 marks]x Form the partial differential equation from z = f( ). y
[3 marks]Solve 𝜕2z +z = 0 given that z = ey, 𝜕z = 1 when x = 0. 𝜕x2 𝜕x
[4 marks]Using the method of separation of variables, solve 𝜕u = 2 𝜕u +u given u(x,0) = 6e−3x. 𝜕x 𝜕t
[7 marks]