Reference no: EM13152441
Q.1 Find a general solution of the following ordinary differential equations:
(a) y' = 3(y+1) (b) y' = y2sinx (c) y' = e2xcos2y.
Q.2 Solve the following differential equations with the given initial values.
(a) y' = x3e-y , y(2) = 0
(b) y'cosh2x + sinh2y =0 , y(0) = -2
Plot the solutions.
3. (a) Solve the following differential equation with the given initial value ( initial value problem:
y' = y/x + 2x3cosx2/y ; y(√Π) = 0 . Plot the solution.
b) Find the general solution of the following ordinary differential equation.
x2y' = y2+xy
Q.4 (a) Solve the following initial value problem:
y' + ytanx = sin2x, y(0) = 1
(b) Find the general solutions of the following differential equation:
xy' + 2y = 9x
Q.5 Solve the following initial value problems:
(a) y' + 3y = 12, y(0) = 6
Plot the solution of (a).
(b) y' + ky, e-kx , y(0) = 0.7
Q.6 Find a general solution of the following system of linear differential equations:
y1' = y1 + y2 .
y2' = 3y1 - y2
Q.7 Find a general solution of the following system of linear differential equations:
y1' = y1 - y2
y2' = y1 + y2.
Q.8 Find a general solution of the following system:
y1" = 3y1 -y2 + 2y3
y2' = -4y2 + 2y3
y3' = y2 -5y3
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