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Bsc CSIT Semester 3 – Numerical Method – Unit 5: Solution of Ordinary Differential Equations (8 Hrs.)

Comprehensive questions and detailed answers for Unit 5: Solution of Ordinary Differential Equations (8 Hrs.). Perfect for exam preparation and concept clarity.

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Solve $dydx=xy,y(0)=1$ , at $x= 0.4$ using Runge-Kutta’s $4^{th}$ order method.

MediumNumerical5 marks2081(TU Final)

Approximate the solution of $y' = 3x^2, \quad y(1) = 1$ using Taylor’s series method using first four terms. Approximate the value of $y(2)$ .

MediumNumerical5 marks2080(TU Final)

Write down the program for solving ordinary differential equation using Heun’s method.

MediumNumerical5 marks2080(TU Final)

Write down the program for solving ordinary differential equation using Heun’s method.

MediumNumerical5 marks2079(TU Final)

Solve the following differential equation for 0 ≤ x ≤ 1 taking h=0.5 using Runge Kutta 4th order method.

y'(x) + y = 3x \quad\text{with} \quad y(0)=2

MediumNumerical5 marks2079(TU Final)

What is a higher-order differential equation? How can you solve the higher-order differential equation? Explain. Solve the following differential equation for $1 \le x \le 2$ , taking $h = 0.25$

\frac{d^2 y}{dx^2} + 3\frac{dy}{dx} + 5y = 0 , \text{ width } y(1) = 1 \text{ and } y‘(1) = 2

HardNumerical10 marks2078(TU Final)

Appropriate the solution of $y' = 2x + y, \quad y(0) = 1$ using Euler’s method with step size $0.1$ . Approximate the value of $y(0.4)$ .

MediumNumerical5 marks2077(TU Final)

How boundary value problems differs from initial value problems? Discuss shooting method for solving boundary value problem.

MediumNumerical5 marks2077(TU Final)

Solve the following differential equation for $1 ≤ x ≤ 2,$ taking $h = 0.25$ using Heun’s method.

y‘(x) + x^2y = 3x, \text{ with } y(1) = 1

MediumNumerical5 marks2078(TU Final)

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