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Q.1 The bending moment, M, of a beam of length l is given by:

dM/dx = w(x+1),

where w is the load constant. If M(0) = 0, find M as a function of x


Q.2 Solve the following separable differential equations:

685_Find the solution of the exact differential equation.png

Q.3. Solve the following initial value problem:

1534_Find the solution of the exact differential equation1.png

Q. 4.Which of the following differential equations is exact:

1802_Find the solution of the exact differential equation2.png

Find the solution of the exact differential equation.

Q.5 Solve the following differential equation with the given initial value.

1994_Find the solution of the exact differential equation3.png

Q. 6. The differential equation : P(x,y)dx + Q(x,y)dy = 0 is not exact. However, if it is multiplied by an integrating factor F(x), it can be made exact. Show that the integrating factor F(x) is given by the solution of the following differential equation:

708_Find the solution of the exact differential equation4.png

Q.7. First find the integrating factor of the following differential equation and then find its general solution:

2coshxcos ydx = sinh xsin ydy

Q. 8. The following ODEs are in the form of y' + p(x)y = r(x), find their solutions.

1006_Find the solution of the exact differential equation5.png

Q.9. Find a homogeneous second order linear ODE of the form of :

329_Find the solution of the exact differential equation6.png

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