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Use Euler’s method with h = 0.25 to obtain a numerical solution of
dy/
dx= −xy2
subject to y(0) = 2, giving approximate values of y for 0 "\\leq" x "\\geq" 1. Work throughout
to three decimal places and determine the exact solution for comparison.
Solve the following difference equation "\\Delta\\lambda^k=-k+5; \\lambda^6=0"
6y^2 dx – x (2x^3 + y) dy = 0 ; x = 1 when y = 1
The wall (thickness L) of a furnace, with inside temperature 800◦ C, is comprised of brick material
[thermal conductivity = 0.02 W m−1 K
−1
)]. Given that the wall thickness is 12 cm, the atmospheric
temperature is 0
◦ C, the density and heat capacity of the brick material are 1.9 gm cm−3
and
6.0 J kg−1 K
−1
respectively, estimate the temperature profile within the brick wall after 2 hours.
Discuss in detail all cases of the roots of a second order linear differential equation with constant
coefficients.
(D2 -2D +3)y = x2 -1
( 1 /t + 1/ t ^2 − y /t ^2 + y ^2 ) d t + ( y e ^y + t /t ^2 + y^ 2 ) d y = 0
(X
