Solve the initial value problem dy/dx = −(2x cos(x^2))y +
6(x^2)e^(− sin(x^2)) , y(0) = −5
Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1
+ t^6)^2 , y(1) = 8.
Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a)
Solve it analytically. (b) Solve it using Euler’s method using step
size h = 0.1 and find an approximation to true solution at x = 0.3.
(c) What is the error in the Euler’s method at x = 0.3
Consider an initial value
problem
?′′ + 2? = ?(?) = cos? (0 ≤ ? < ?) , 0 (? ≥
?)
?(0) = 0 and ?′(0) = 0
(a) Express ?(?) in terms of the unit step function.
(b) Find the Laplace transform of ?(?).
(c) Find ?(?) by using the Laplace transform method.