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Bsc CSIT Semester 1 – Mathematics I – Unit 7: Ordinary Differential Equations (6 Hrs.)

Comprehensive questions and detailed answers for Unit 7: Ordinary Differential Equations (6 Hrs.). Perfect for exam preparation and concept clarity.

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\quad$ (a) Find the solution of the initial value problem

x^2 $ y′+xy=1, y(1)=2, x>0.

$\quad$ (b) Find the area enclosed by the line y=x−1 and the parabola $y^2$ =2x+6.

HardNumerical10 marks2081(TU Final)

Show that every member of the family of functions $y = \frac{1 + c e^t}{1 - c e^t}$ is a solution of the differential equation $y' = \frac{1}{2} (y^2 - 1)$ .

MediumNumerical5 marks2081(TU Final)

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Sample Questions

$\quad$ (a) Find the solution of the initial value problem $ x^2 $ y′+xy=1, y(1)=2, x>0. $\quad$ (b) Find the area enclosed by the line y=x−1 and the parabola $ y^2 $=2x+6.

Marks: 10Chapter: Unit 7: Ordinary Differential Equations (6 Hrs.)

Show that every member of the family of functions $ y = \frac{1 + c e^t}{1 - c e^t} $ is a solution of the differential equation $ y' = \frac{1}{2} (y^2 - 1) $.

Marks: 5Chapter: Unit 7: Ordinary Differential Equations (6 Hrs.)

Bsc CSIT Semester 1 – Mathematics I – Unit 7: Ordinary Differential Equations (6 Hrs.)

Sample Questions

$\quad$ (a) Find the solution of the initial value problem \( x^2 \) y′+xy=1, y(1)=2, x>0. $\quad$ (b) Find the area enclosed by the line y=x−1 and the parabola \( y^2 \)=2x+6.

Show that every member of the family of functions \( y = \frac{1 + c e^t}{1 - c e^t} \) is a solution of the differential equation \( y' = \frac{1}{2} (y^2 - 1) \).